Boss Battles typically occur every 5 mission chapters. Winning a Boss Battle will usually award Credits, a Decoy, and a bound or unbound Power Pack or Energy Pack. Event missions also have a Boss Battle every 5 mission chapters up to Mission Level 100.
These battles are fought with your leader. You can also choose two people from your friend list. You can use power packs during the Boss Battles' to replenish your defence.
These battle have 2 steps. Step 1, you and your friends' cards attack the boss. Step 2, the Boss attacks you and/or your friends cards.
Occasionally, you will obtain the card of the boss you defeat. This usually happens after you've defeated the boss for the last time in the mission story.