a) do not allow the enemy to collect three stones,
b) collect three stones to start inflicting serious damage,
c) postpone unleashing your special attack until the power bar is nearly depleted.
Is there something else I should be aware of first and foremost? Some hint like "Gunvalkyrie - stay airborne"? Normally, I like to find such clues in manuals, but no manual for me this time. The guide I linked to explains techniques, but 2 gets so busy from the word go I end up bewildered every time. Funny how it looks like a "party game", but without a companion to share my confusion, I have a hard time learning how to play.

Last but not least, is Team Battle the only co-op mode?