Typical reaction upon first seeing the Daedalus Attack: "Dude, did the Macross just punch a battleship in theface?" Considering that the arms of the SDF-1 are spaceships, it's literally punching battleships with battleships.
Interestingly, we know that Vrlitwhai and Exedore had that same reaction. Followed by summoning reinforcements.
Misa gets her tactical moment, coinciding with the Macross' super robot moment in Ep 06 "Daedalus Attack". After the main gun fails to fire due to the interference from the pin-point barrier system, Misa gets the pin-points to concentrate on the bow of the Daedalus (right arm) and punch through the bow of Zeril's battleship. The Daedalus opens up and all 587(!!!) destroids open fire into the innards of Zeril's ship. No other anime has this and no other should.
The Robotech novelizations turn the Destroids dying horribly in Khyron's assault on the earthbound SDF-1 into an awe-inspiring heroic last stand as the Destroid pilots try to buy time for the VFs and MAC/Monsters to arrive; they also include a scene of the Destroids marching out to back up the SDF-1's turrets in the final battle against the Zentradi fleet that was not in the anime, describing it loving detail and crediting them with tripling the SDF-1's short-range firepower for the last battle.
Hikaru's moment comes during the epic "Force of Arms" "Love Slips Away" episode, which starts with the near-destruction of Earth and ends with the destruction of the main Zentradi fleet. While his Valkyrie disintegrates, he returns to Earth to rescue Misa.
And, of course, the "Do You Remember Love?" final attack run from the namesake movie is a Crowning Moment for the whole medium of anime.
Breetai gets thrown into space in the episode where Hikaru boards his ship. Breetai manages to walk across the ship to another airlock and then beat down two Valkyries with a pipe.
A UN Spacy Zentradi infiltrator soldier makes a fake distress call to Kamjin and gets his cigarette lit up by allowing a Valkyrie fire his assault rifle in order to use the muzzle flash as light.
The first, and last, stand of the Grand Cannon lives up to its name even if it was to be useless in the long wrong. The novelization makes it a little more delicious by stating that the Zentradi never lost so many ships so quickly.
Maximilian Jenius' first battle Super Dimension Fortress Macross/Robotech. When Kakizaki fails to live up to his boasts and has to be rescued by Hikaru, the two lose track of the more modest Max. They find him destroying battlepods left and right with deadly ease.
It should be noted that the above battle was Max's first ever combat mission, and yet he downed nearly twice the number of enemies as his commanding officer, series protagonist Hikaru Ichijyo.
Max gets a second in Macross 7, where he orders the Macross Cannon fired. At empty space. When queried on it, he replies with something along the lines of 'call it the intuition of a genius'. The cannon is fired and an enemy battlegroup folds in directly in the path of the beam. Made this lurker's jaw drop at the sheer awesome.
Also notable in Macross 7 for absolutely stealing the spotlight from Gamlin's 'death' by folding directly into the middle of a stalemated battle, outflying every single ace in his space-force (despite being in his 50s), shooting down just about all the enemy VFs, flying down a tunnel while being shot at with lasers, and bulls-eying the Big Bad in his secret lair, all within about 30 seconds and without anyone understanding who had just shot down the entire enemy force.
Let's not forget that in-universe, Max is the first person to marry a hot alien babe, who gave birth to seven (!) daughters.
The way he proposed to said wife also counts, she attacks him with a knife and Max disarms her and then asks her to marry him.
Don't forget their marriage either. Remember the scene at high-profile marriages where a line of guys cross their swords above the couple? Macross does it with Valkyries in Battroid mode crossing their guns' muzzle flashes. And don't forget about the Macross-shaped cake either.
Oh, and the jaw-dropping dogfight with Milia, both in the series and The Movie. Max came out on top in both cases, proving that by beating the best Zentradi fighter pilot (a female no less), he's technically the best pilot in all the Macross universe.
In one of the Robotech: The Sentinels novels, he and his daughter Dana fight. The fight is interrupted before it concludes, but it's implied that she may have managed to beat him if they'd fought to the finish.