Here is the full list of all 9 OctaFight trophies - there are 5 bronze, 2 silver and 2 gold.
Start a party with all game rules in Full Random
Start a party with 4 players
Start a party in Team mode
Succeed a PerfectShield
Visit the shop, and buy something
Succeed a revenge match
Taunt just before the end of a round
Play 100 matches
Win a round without killing anybody