Here is the full list of all 18 In Space We Brawl (EU) trophies - there are 16 bronze and 2 silver.
Kill 4,000 aliens
Kill 250 players with the Quantic Slinger
Obtain Old School achievement 50 times
Kill 50 players without using weapons
Kill 250 players with the Plasma Sword
Commit suicide 50 times
Play 100 mirror matches
Win 25 1 vs 3 matches
Complete all the challenges with S rank
Complete all weapons challenges
Complete all the 21 challenges
Complete all spaceships challenges
Complete 10 matches in less than 3 seconds
Collect 5 defensive pods at the same time
Fight in every single sector of each location
Complete 1000 fights
Fire 500,000 shots
Kill 2,000 players