How can you get sonic adventure 2 battle on ps2?

You can't get Sonic Adventure 2 Battle on PS2.

Sonic Adventure 2 Battle was exclusively released on the GameCube.

You might be thinking of Sonic Adventure 2, which was originally released on Dreamcast and later ported to GameCube, PlayStation 2, and PC. However, the "Battle" version was a GameCube exclusive.

To play Sonic Adventure 2 Battle, you'll need a GameCube and a copy of the game.