An undisputed Crowning Moment of Awesome is when a person is able to level up their unit to OC-EX, which is basically the level cap for mobile suits. Not only does this mean they've maxed out their unit's skill points to make it as dangerous as possible, but upon reaching OC-EX they're allowed to pick another boost to a specific stat. Reaching OC-EX takes a lot of time and effort, even for C-Ranks, so it's such a big deal when it happens that a message goes out to the whole game when you've accomplished it, letting everyone know your Mobile Suit has reached its maximum potential. Becomes even more awesome the higher ranked the unit is, which affects how much EXP each level requires and your odds of successfully reaching another over-custom level.
It's a CMOA when a player is able to take down an enemy player using a suit with a lower rank than the other player, proving superior skill and ability. Bonus points if the opposing player has an advantageous property.
Curb Stomping the other team in any gameplay style, but especially Grid and Death match styles.
In an inversion of the above example, going One-Man Army on the opposing team when you're outnumbered and outgunned, yet still able to come out winning.
For the American Servers, it's getting OG Planet to own up to a massive mistake on their part. To wit, players were lead to believe that OGPlanet's free Astro system had jacked up the number of Astros to be earned and many flocked to reap the freebies. However, OGPlanet discovered this and quickly reduced everyone's totals to where it should be, even taking back legitimately purchased Astros. And people were livid. For a straight month, while others in the rest of OGPlanet's games had seemingly moved on with their lives, those in SDGO refused to bow down, leading to OGPlanet giving the players in all of the games a reward of sorts determined by how many Free Astros they lost and restoring the legitimately purchased Astros.
Whenever you're able to kill one or more enemies with your special is always awesome, particularly if it's a kill that really counts.
Any time you were able to counter a special attack with your own.