Game Breaker: The Gargoyle mech. It has a nigh-unblockable aerial throw and decently powerful attacks, and a shoryuken with the most ridiculous invincibility frames ever. To make matters worse, it can chain the air throw out of the shoryuken. Oh, did I mention that everyone online plays on Hyper Mode which makes the game moreStreet Fighter, giving rise to the impossibly powerful 'Triangle Jump' technique? Ironically, Gargoyle's countpick is Jaguar, mediocre at best (it's the starting mech in tournament mode), though This Troper swears by it.
The Chronos has a combo that involves using its time freeze projectile, attacking the opponent while their frozen and knocking them into the air, so you could time freeze them again, and knock them in the air while they were helpless. If timed right, this combo is pretty much unstoppable and makes even the Ultimate Mode seem like a joke.
See also the Katana. Not gamebreaking unless it's playing with all upgrades--in which case it has the stupidly powerful Fireball projectile and a five-hit Shadow Rising Blade rush which it is completely invincible for the duration of.
We also have the Shredder, who is above average at best until you click over to Hyper Mode. As game guru Robyrt put it, "If you land a flipkick or headbutt with Shredder, your opponent should die".
Also, some of the possible combos (Robyrt has some cool ones on his site) are flatly ridiculous. Against a suitably slow opponent with a suitably fast pilot, Jaguar can chain two Overhead Throws (air throws that hurl the opponent across the screen, in a game without dashing) together. And the Nova can use its aerial bellyflop, which knocks down an opponent, and chain it into the grenade...then hit the opponent as they get up, knocking them back into the grenade. Similarly to Jaguar, it's possible for Flail to chain its Spinning Throw into itself, but that is even MORE ludicrous, as it sends them flying almost on the ground.
Gargoyle is technically the best robot, but it requires you to have consistent execution. Electra, on the other hand, has stupid good punch attacks, one of which can lead to an infinite if your pilot is fast enough. This troper would say Electra is more of a Game Breaker than Gargoyle.