Everything about the buildup and execution of the duel between Altera and Gilgamesh in Chapter 2 of the Dawn Arc. Hakuno is so impressed by her willingness to take on the King of Heroes that s/he begins to fight for her willingly from then on and take back the position of Master in the process.
Earlier on Jeanne also gets one for not only surviving against Altera's attacks but tanking and surviving Gilgamesh's Storm of Blades without any time to react.
Gilgamesh getting a Big Damn Heroes moment later in the Dawn Arc. While text doesn't get the sheer badassery of it as seeing it on screen, it gives a good idea:
Archimedes: Perfect. That's it. Just right.... You're nothing but a powerless doll, Sephyr. Altera: ...I wouldn't say that. Archimedes: *gasp* -Gate of Babylon opens behind him and dozens of weapons fly out, assault him from behind- AAAGGGH...!! Gilgamesh: Your arrogance betrays you, Archimedes. Licking your chops in front of your prey as if you're already at the top of the food chain. Your insignificance amuses me. Or did you think that you had the world right in the palm of your hand? If so, you truly are the greatest. The greatest of fools. *laugh* I cannot stop laughing! Take this as a reward! Receive my treasured swords! Archimedes: ... King of Heroes?! Impossible. Why would YOU stand in my way?! Did you not say you owed Altera but a single favor?! Gilgamesh: Yes. Indeed I did. In accordance with the ancient contract, I would serve the White Titan once in her time of need. But you fail to understand. I did not settle for being second command for Altera's sake. It was for that foolish character... I was lending my power to Hakuno Kishinami. Never to Altera herself. And if that's the case then... well, technically, I believe I'm still under contract to Altera, since I have yet to save her.
Gilgamesh proves why Gate of Babylon can't be blocked or be properly defended from by using mere shields by overpowering Archimedes' own shield with just one use of his trademark Noble Phantasm which causes said Big Bad to question Gilgamesh's motivation to 'protect' Altera.
Hakuno's recollection of the Dawn Arc and immediately calling out Archimedes on his scheme at the start of the True End route.
Gilgamesh again: His Side Story final chapter has him face off against Nero, then Artoria. The only thing that would have made such a battle against both Sabers even better is if he'd taken them on at the same time.
Artoria's side story ends with her confronting both Iskandar and Gilgamesh at the same time. Fans with knowledge of previous Fate works will remember that these two once called her ideals about kingship wrong and that she was not worthy of her title. Well, now she finally gets to have a bit of payback by defeating two of the most powerful Servants in the Moon Cell by herself.
A minor one, but Nameless' iconic theme song playing when he's the boss servant is definitely worth a mention.
Each of the first three routes pits you against some bosses who you're told to not attack due to certain conditions: Nero's has Lu Bu in Stage 2 (Nameless will repeatedly say to avoid fighting Berserker as it will lead to trouble but either he or Nero will congratulate you on defeating Lu Bu if you defeat him without taking the other sectors), Tamamo's features Gawain in one chapter (Karna states that due to Lu Bu's legend of being a powerful warrior that he can stall Numeral of the Saint-buffed Gawain for time and tells you to lure Gawain to Lu Bu until you do so) and not long after there's Altera herself (Karna recommends avoiding her as she's too powerful to overcome), Altera's has Nero in her Regalia Mode (makes sense as Regalia Mode prevents the Servant from flinching from being hit and Gilgamesh says that it's best to use your soldiers as bait while you take out the other sectors to lure out Gawain), although in the case of facing Nero, she's not the issue. You have to complete your Regime Matrix before the timer runs out then defeat Gawain and whenever Nero seizes a field, she takes off in your direction. This also comes down to the fact that just like in Tamamo's route when facing Gawain, Nero's Regime Matrix is almost complete so you need to avoid fighting her to regain control of the battle. It feels pretty awesome when you manage to defeat any of them when you're told not to though.
Then again, when playing Tamamo's route, in an equal aspect Berserker Lu Bu despite being the NPC ally gets some equal credit. When facing down a super buffed Gawain who will target you until you lure him to Lu Bu, you are told repeatedly by Karna (until you do as what he says) to bring Gawain to Lu Bu as the latter is strong enough to fight the former to a stand still. This shows as once you do, Lu Bu does stall Gawain until you take over the needed sectors (this is adding in tension as during the start of the mission the enemy's Regime Matrix is almost complete making it so you really can't fight Gawain at the moment as you need to regain control of the Regime Matrix to avoid losing), then you repay Berserker by defeating the Knight. A few chapters later when you first face off against Altera's forces, who is facing a 'nigh-unstoppable' Altera? It's Berserker Lu Bu and his defenses give you enough time to take over at least 2-3 sectors to help balance out the Regime Matrix so you don't get rushed too hard if Tamamo/Karna is strong and fast enough before he gets defeated.
While his status kind of makes it clear, Karna's Side Story is essentially performing Tamamo's route but without any support from Caster. You first stomp through the entirety of Nero's army, first her generals then Nero herself but then you proceed to do the same to Altera's army just to stop Sephyr. Yes, one Servant who is acknowledged to be Gil's only rival in Fate/Extra CCC effortlessly takes down two armies just by his own power. While some of the opposing Servants on said armies can't compare to him in terms of power, the others such as Cu, Altera and Gil do pose a decent threat and he still beats them. In the end he stares down Sephyr who's going to try to destroy Karna and states that even though those before and after him might not be able to defeat this threat, he will not allow Sephyr to continue on her rampage and that he will win this battle. Thanks to the circuit line at the end of his story shining and continuing up, Karna most likely won that battle making him one of the few Servants who have a story based on fighting Sephyr to defeat Sephyr without any support (minus from the Master). Normally when you face Sephyr in story missions, you have your faction leader and their lieutenant (if you have a Code Cast that allows swapping Servants that is).
Nameless' Side Story finale involves him fighting Artoria. Even if Nameless isn't the same as F/SN EMIYA, we know that the latter couldn't defeat Saber in the Fate route. Here we see Archer defeat Artoria after having to force Rider off the map (three times in a row thanks to Iskander retreating twice before finally being defeated) followed by dealing with Ruler. Even better, since Nameless like EMIYA are based off of Shirou Emiya (they originate from Shirou himself but the later outcomes that result in EMIYA and Nameless differ), you allow Archer to defeat Artoria in a fair fight where the original Shirou himself said he was never able to do so on his own.
If this were an actual war that more realistic conditions would apply, Nameless would be near exhausted from fighting Rider thrice then Ruler right in a row not taking fighting and regaining control of other sectors into the equation. Granted that the former is quite durable as shown in Fate/Zero and the latter was shown to briefly survive a nuke from Lancer of Red in Fate/Apocrypha, this is quite a feat when you should be tiring out from rushing from one area to another without rest. However, Artoria is his final opponent and she's well known to be quite a powerhouse herself and to make things even more intense, she's in prime condition unlike Nameless who is probably a bit ragged. To defeat three Top Servants (with the final one being perhaps over thrice as strong as the first one) in just one sitting while trying to give your faction the win and you are doing it by yourself and when you aren't the strongest of your team is very much badass to the highest possible level.
And if you learn about his backstory, he's even more of this. His Extella/Zero version - with his body half collapsed and the other half burned to the point that Nero and Tamamo don't recognize him - managed to help the female version of Hakuno - who had no soul, hence why Nameless is incomplete - reached her 7th Round. And their opponent for the 6th Round is none other than Leo, meaning that a weakened Nameless fought Gawain and WON. And there's implication this version of Nameless went through the same events but actually won the war with Female Hakuno.
It mixes with both heartwarming and tearjerker but in the final segment of Nameless' Side Story, he tells Archimedes that he lost to Altera in his own timeline and after the Archimedes leaves, Nameless mentions that the Hakuno of this timeline didn't 'fall in mid-battle' alongside him back in his own timeline like his former Master, Female Hakuno. Yes, out of sheer devotion and concern to Female Hakuno, a very worn down and burnt out Nameless decided that he would attempt to do the impossible in order to give Female Hakuno some more time to live. What does he attempt to do? Fight his timeline's version of Altera to the very end. Although both he and his former Master lost their lives trying, it's no less badass that he, someone with little legend or anything very powerful fought for a long time against one who is considered by Tamamo who is a fragment of the Sun Goddess Amaterasu of all beings to be a 'Destructive Force of Nature' and even she saw that facing down Altera/Sephyr was pointless for the majority of the game since Altera's sheer power is overwhelming even by Servant standards and as the White Titan, that power is multiplied even more. Let's not forget that Nameless, just like EMIYA is Shirou Emiya. This doubles the amount of awesome that someone who was considered a poor magus in overall terms of potential in the past put up one last strong fight against someone who is far more powerful than nearly every other Servant in the series without backing down.
Gawain's Side Story can potentially end with him fighting Iskander and Artoria at the same time, and doing so is immensely satisfying. Doubly so since Artoria doesn't want him to hold back in order to show her how much he's grown, because she's not about to either.
Iskandar. While it triples as awesome, heartwarming and tearjerker, Iskandar stands out as remaining as who he most likely was back in Fate/Zero. His debut in the game is awesome and you even get to fulfill the role of 'King of Conquerors' in his own Side Story where in the end it looks like his ending is the opposite of Altera's when they first squared off, literally meaning that he's actually winning against the one who beat him in the story (even if he was holding back most of his power as Altera pointed out). Awesome character who stands out to where in each story, faction leaders tend to break down emotionally when they're about to die or when facing death. Iskandar? When defeated by Nero who he accepts as a worthy opponent (Nero likewise agrees and is enthusiastic to battle such a famous hero), he's still standing and starts laughing happily on how great his final battle was before disappearing. Of course this is also heartwarming that his character remains unchanged virtually and offers some good advice to Nero yet sad that he has the only real death out of all the Servants in the True End route.
Even if she couldn't slow down the fall of the Umbral Star's Starship, Titan Altera gets one in the True End route. As the starship comes hurtling towards them at a speed where Hakuno mentions is too fast to divert off-course, both Hakuno and Nero are feeling desperate as they feel powerless to stop it while Archimedes cackles in laughter nearby. Then Titan Altera shows up out of nowhere and places all her strength into a single punch to try to stop it, even though her attempt fails, Hakuno notes to themselves that that punch could easily have caused more damage than they could ever imagine to anything it made contact with which sends a shiver of fear and dread through them. Her appearance also gives Hakuno and Nero another chance to win and gives them confidence that there's still hope to complete their true mission meanwhile Archimedes goes through another harsh villainous breakdown just seeing Titan Altera show up to ruin his plans yet again.
Altera knows a lot about every other Servantnote she doesn't know a lot about Gilgamesh which is funny because according to him, her legend as the Sephyr predates his legend as the 'King of Heroes/Oldest Heroic Spirit' and she has no clue on who Nameless really is since he lacks a legend for himself and when she asks him for his real name, he merely responds that he has 'no name' just like her. She is often The Dreaded in-battle due to her ferocious combat skills and most Servants take her seriously. However while she is The Dreaded to most of them, Artoria is The Dreaded to her. Yes, Artoria is the only actual Servant to make Altera become truly scared in battle as an opponent as the only other being she fears is herself becoming Sephyr. Funnily enough she remembers Artoria's divine sword Excalibur but not hernote With the implication being that someone else wielded Excalibur against Sephyr. Oddly, Artoria herself mentions in her first Side Story mission that she recalls a 'titan-sized destroyer' that was causing chaos and destruction to her homeland/Britain in the far past so it might be that Hero Altera recalls a 'different' Artoria and not the one she is currently fighting. Her brief conversation with Artoria shows her losing her calm and preserved personality:
Artoria: You know of this sword...? Have the stories reached even your people, then? But...
A smaller one for Nero near the end of the Flame Poem Arc when she deduces Altera's identity that the people on Earth knew her as: Attila the Hun.
In the True End, not that long after Mind Hakuno and Nero arrive at Tamamo's Millennium Castle, do you meet Caster herself who addresses the 'you', aka Mind Hakuno as her husband much to Nero's minor frustration. It looks like things will play out just like Nero's Flame Poem Arc encounter but it doesn't go that way.
1) Both Mind and Soul Hakuno nod in agreement on what has to be done and merge together much to their Servants awe. Afterwards it becomes funny since both Servants are arguing about who's your true Servant and your 'Soul' aspect talks to Caster to let her know that you (the Soul) is still here.
2) Altera (in her Hero form) shows up just like how she did when she first met Nero in her own route. Before she shows up the 'sky' starts to crack and distort resulting with Nero cementing that their real fight has started to begin followed by Tamamo saying that 'she's' about to appear. Once Altera shows up and after she gives her normal 'destruction' speech, does the enemy Saber speak to both of your Servants that she'll defeat them and take the Merged Hakuno as her 'slave' although Nero and Tamamo disagree. Merged Hakuno then narrates on how their Servants aren't showing any fear or hesitation to fight Alter even though the odds are greatly against them and that Body Hakuno (of this timeline) must be in the Regalia that Altera holds.
3) When Altera starts to attack, Merged Hakuno does something that seems very dangerous and uncalled for by means of being a Master. They move in front of both Nero and Tamamo and act as a shield to prevent Altera from killing them, this causes both of said Servants to have a momentary freak out that their Master is risking their lives for them like this (Mind Hakuno told Nero earlier on in the same route that they would protect her at all costs to avoid losing her which is very much heartwarming). Then Altera attacks but fails to harm Merged Hakuno as both Nero and Tamamo each activate their Regalia to shield their Master (both of them mention that Altera's not showing any signs of negotiating and desires to fight) before Nero recalls them to her ring much to Tamamo's dismay.
4) Then comes the very first epic turnaround in the game, Team Tag-Battle and they declare to Altera that she now fights the two of them at once. You then play as Nero with Tamamo as an ally and the two of you then deliver one crazy battle before giving Altera her first defeat in this timeline. Of course Altera gets a bonus for being awesome in that the battle didn't really even weaken her at all and for the most part she was unfazed by two very strong opposing Servants.
playing when he's the boss servant is definitely worth a mention.