Here is the full list of all 12 Hyper Jam trophies - there are 8 bronze, 3 silver and 1 gold.
Deal all of the damage in a round
Win a match without equipping a weapon
Survive a round without dealing damage
Win a match using a single weapon
Start a round with 200% health
Kill an enemy on full health with a single hit
Win a 4-player match by killing every player in the final round
Get a hammer kill on a falling opponent
Stop a final round with a laser strike
Parry a projectile into an opponent, killing them
Get a kill after you die
Survive 3 times in a round using the Survivor perk