The Enterprise dropping out of the Aquatic Ship's launch bay into a major battle with the Reptilian Xindi.
Archer being interrogated by Commander Dolim. Not only does he change the subject of conversation from how many Earth ships are in the Delphic Expanse to dinosaurs, but he delivers a killer ice burn to the Reptilians:
Archer: I'll bet you didn't know this...but at one time, most of my world was ruled by reptiles!
Dolim: (Intrigued despite himself) I wasn't aware of that.
Archer: A comet hit, about 65 million years ago. Caused a mass extinction. Most of the reptiles died out—mammals became the dominant species.
Dolim: How unfortunate.
Archer: Still, the reptiles might have come out on top, if it weren't for one slight disadvantage!
Dolim: And what was that?
Archer: They had brains the size of a walnut. (Beat) That's very small. (Beat) Apparently, it's a constant in the universe.
Dolim: (Hand lunges out—visibly resists the urge to strangle Archer)
Archer then goes on to talk about how one of his favorite dishes is turtle soup—which finally causes Dolim to lose his cool completely.
The Mirror Universe ISS Enterprise. The scene where Commander Archer and his team storm the Tholian complex and literally ship-jack the Defiant was priceless.
Don't forget the scene where they make it to the Defiant's bridge and boot up the ship's computer. The camera panning lovingly over every station as they power up and all the TOS bridge sound effects come in one-by-one... Wonderful.
The Defiant going into battle was surprisingly Bad Ass. Long-time fans of the show remember the Constitution-class ships (e.g. the TOS Enterprise) firing phasers at other ships in a pathetically weak manner. The Defiant's phasers, on the other hand, rip the Tholian and ISS starships to shreds.
The whole sequence is a meta-CMOA for the creators and effects people, proving that it is possible to make the Original Series aesthetic still look credible and badass here and now.
In all fairness, the 'In A Mirror, Darkly' theme is awesome simply by virtue of having a theme slightly (and perhaps ironically) more reminiscent of the OST series.
For the show as a whole, just about the only thing anyone can agree on is how awesome "In A Mirror, Darkly" is.
Ironically, despite being the chief engineer, Trip gets his when he is in command of Enterprise during the episode "Cease Fire." Archer and T'Pol are on a planet disputed by the Vulcans and Andorians. While they're trying to negotiate a cease-fire without being killed, the Vulcan and Andorian fleets are about to start shooting at one another in orbit. They each advice Enterprise to withdraw. Instead, Trip targets both fleets, threatening to open fire on whoever fires first.
Trip and Soval each get one in the episode where they warn the Andorians about an impending Vulcan invasion of Andoria. Soval's is when Shran is torturing him with a device that removes Soval's emotional control and in order to convince Shran that he's telling the truth, Soval says something to the effect of "Then turn it to a higher setting already." Trip's comes when Administrator V'Las tries to get them to back down, Trip informs him that Starfleet has been told what Enterprise is doing, so they will know who destroyed Enterprise.
Also from that story, Soval telling Archer to do whatever it takes to find out the truth behind the bombing, with his full support.
Shran: "The Andorian Mining Consortium runs from no-one."
Contacting Enterprise in the middle of a huge battle just to say "Tell Captain Archer that's TWO he owes me!"
A female MACO gets one in "The Xindi" while trying to break Archer and Trip out of a mining complex. A big alien attacks her from behind and knocks away her gun. She pulls some martial arts moves, takes him down, then rams her stunstick into his back for good measure.
The augments in the opening to "Borderland" provided a villainous example: two of them, completely unarmed, are "captured" by the Klingons, and then as they're being escorted to the brig, proceed to wipe the walls with the entire crew. One look at that opening, and it becomes obvious that the Klingons' desire to make augments of their own in the later episodes "Affliction" and "Divergence" was not merely a case of male-hormone-driven jealousy. Had there been a few more of them, one can see how the human augments really could conceivably have overthrown the entire Klingon Empire.
Trip's true moment would certainly have to be in the fantastic episode "Terra Prime." He was held captive by the terrorist group Terra Prime. Part of the story involves this group cloning a half-human/half-Vulcan from Trip and T'Pol. After his guard insults his daughter, Trip tenses up and the more physically intimidating guard notices. He taunts him, saying "Go ahead and try." Trip begins to back down, then says "Okay!" and uppercuts the guard.
Including Archer killing a Reptilian Xindi with a bronze sculpture, T'Pol ramming the Xindi ship attached to Enterprise into another Xindi ship, Phlox developing a cure for Archer that involves shooting him full of antimatter, and all three of them blowing up the ship to erase the timeline that necessitated all of the above.
Let's not forget the harrowing destruction of Earth that starts the whole thing.
The Xindi engineer Gralek's speech to Archer in "The Shipment" deserves to be quoted:
Gralek: I'm proud of my craft, Captain. I've practiced it for many years. I won't see my work corrupted in this manner. Seven. Million. People.
The entire two-parter "Affliction/Divergence" is one for Phlox as he tries to create a cure to the Klingon plague under increasingly difficult and tense circumstances and succeeds, capping it by stopping a Klingon ship from destroying the colony by beaming the virus on board and blackmailing them into backing off.
And then there's Trip transfering from Columbia to Enterprise by crawling along a tether between the ships at warp speed, then rebooting Enterprise's warp reactor just in time to keep the ship from blowing up.
Captain Archer's final no-holds-barred fight with Commander Dolim in "Zero Hour". As one Youtube commenter puts it, it's the "best kill by a Starfleet captain. Ever." Nobody in a Starfleet uniform other than Worf has dispatched a foe in a manner so bloody, and so AWESOME.
T'Pol calling John Frederick Paxton on his hypocrisy in "Terra Prime".
Archer telling Duras to go to hell and cutting his transmission. Most Starfleet Captains would try to reason with the angry Klingon threatening to kill them. Jonathan Archer is not most Starfleet Captains.
Not true, a good few captains would've also told Duras where to stick it, among them, Sisko, Janeway, Kirk, and Picard. But it just shows the kind of good company Archer is in.
Actually the moment of badass is that he tells the angry Klingon to shove it and then proceeds to blast his battlecruiser to shit. Complete with some neat piloting from Ensign Mayweather.
Shockwave, Part II. That episode featured some truly cool moments for the crew.
Captured by the Suliban and held prisoner in a nebula, it seems that the Enterprise crew has opted to just blow up their ship. The Suliban tow the ship out of the nebula into empty space just as it's warp nacelles are bursting into flames. As soon as they leave....the flames suddenly cease, the nacelles get ethereal glow, and the Enterprise blasts off into warp speed! Trip Tucker had faked the warp core breach just so they could escape. Badass Engineer? Damn straight!
Captain Archer delivering a quick beat down on Smug Snake Silik.
"I SAID you're an ugly bastard!!!!
"You're going to call off your ships. And then you're going to giving me back those data disks you took.
It might have been a piece of scenery, but the "Carl Sagan Memorial Station" on Mars in Terra Prime was awesome. Great quote, too:
As much of a Base Breaker as "These Are the Voyages..." was, the final scene, with Captains Picard, Kirk, and Archer sharing The Speech, was awesome. To the point where fans who disown every other part of "These Are the Voyages..." won't disown it.
In "Proving Ground," after Shran has revealed his duplicity and gets a little smug about it, Archer decks him.
"You like to talk about repaying debts? I've owed you that for a long time."
In "Storm Front", there's the climactic battle with Enterprise dueling Nazi warplanes over New York City.
The Reptilian Xindi abduct Hoshi and use brain parasites to force her to decrypt the Aquatic Xindi activation codes for their superweapon. When she gets access to the code, she fights off the brain parasites, re-asserts her willpower, and adds even more encryption. When Dolim realizes what she's doing and drags her off for a second dose of brain parasites, she tries to throw herself to her own death. It doesn't work, and in the end, she does decrypt the access code, but by then, The Cavalry has had time to show up.
Archer's epic "The Reason You Suck" Speech to the hostiles in Season One's "Silent Enemy". The fact that he ends the speech (which is seen entirely via an alien viewscreen) by firing a phaser at the hostile's recorder—punctuated by a switch to static—is a Crowning Moment Of Awesome for the whole episode.
In a sense, the episode itself is a big "Took a Level in Badass" for Archer and his crew—especially in that relatively early point in the show.
Early in "The Expanse", the Enterprise is attacked and easily disabled by a Klingon Bird-of-Prey, and is only saved when reinforcements arrive to drive the Klingons away. Enterprise is refitted throughout the episode for its dangerous mission in the Expanse, and among the improvements are a cache of brand-new photon torpedoes and no less than seventeen additional phaser cannons. When the Klingons came calling again, they were … unprepared, to say the least.