All I gotta say is, what a match, ladies and gentlemen, what a match. Let me go over the characters right quicklike:
Yuki Showings:
-Yuki is pretty much The Host lite. There's a stronger being in her universe and some of her feats are questionable, but she exhibits very similar abilities to him otherwise, sans the metafictional powers and dealing directly with concepts.
-Her future selves informing her is debatable - depending on your opinion of MPFC neutrality the future selves do not exist in this continuity, stripping her of her nigh/total omniscience. This isn't a showing, but it bears clearing up so nobody makes odd assumptions.
-She has stopped time before. Nothing more need be said here.
STTGL Showings:
-Has achieved literally impossible things before. The more hot-blooded the pilots get the stronger the Lagann becomes. The famous song Libera Me From Hell isn't exaggerating when it says "touch the untouchable, see the invisible". With enough willpower STTGL can do that.
-Has grown to the colossal size outlined above. There's no reason to believe it couldn't get bigger, either.
-Defeated the Anti-Spiral by overwhelming it with fighting spirit. He forfeited, but only due to fear of what might happen if he and the STTGL kept fighting. STTGL is presumably slightly weaker, but still powerful beyond measure.
-EDIT: Super Giga Drill Breaker in action. A showing of power for STTGL:
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Currently playing: League of Legends, Chrono Cross.
Current Projects: Fool's Overture, CYOA: http://www.gamefaqs.com/boards/8-gamefaqs-contests/60143513