Level select:
You must beat the game twice.

Team power option:
After getting two head shots in a row and then check the Battle Mode screen.

Custom option:
Achieve 100% hit head shot status twice in a row and then check the Battle Mode screen.

Humans and creatures option:
Upgrade one of your character's weapons to the fullest then check the Battle Mode 'team types' screen.

Defeat leader option:
With all your team members health at 100% beat an episode and then check the Battle Mode 'objectives' screen.