Batman is one of the greatest strategists in the world of comics. His prep time is legendary for being able to empower him to beat foes that are infinitely more powerful than him.
Now, we are not going to pit Batman against Super Tengen Toppa Gurren Lagann because that would be spite - Super Tengen Toppa Gurren Lagann is universal level in power which Batman definitely has no solution against, so we have to settle for TTGL who is of much lower power level.
So long a character isn't universal, Batman has a chance of outwitting that character I would believe.
So with 20 years of prep, is Batman able to figure out the mystery of spiral power as well as know the Gurren Lagann team inside out in order to take down Tengen Toppa Gurren Lagann? Discuss! :)
UPDATE: Batman has 20 years of prep, knows about the Gurren Lagann team, and has access to the technological resources in the Justice League tower. But he has no allies to help him. Because this battle is a test of whether Batman can use his brains and figure out the weaknesses of what seemed to be an omnipotent mecha (Its not).