Here is the full list of all 12 Battle Trivia Knockout trophies - there are 8 bronze, 3 silver and 1 gold.
Win a single match
Get fourth place in a full length game
Knock out your opponent with a KO
Win first place in a full length game
Get 5 answers wrong in a single battle round
Win 1000 points or more in a single wager in Wise Wagers
Earn 20000 points in a full length game
Get 15 questions correct in a full length game
Use all 8 taunts in a single full length game
Answer all 5 questions correctly in a single battle round
Flip 3 point tiles in a row in Tiles of Death
Complete a single match game