Here is the full list of all 10 #KILLALLZOMBIES (EU) trophies - there are 3 bronze, 6 silver and 1 gold.
Kill 500.000 zombies.
Stay alive at least 60 minutes.
Explode atleast 100 cars in one session.
Rack up to 30 level.
Get 10.000.000 experience points in the single session.
Kill at least 1.000 zombies with each weapon type.
Kill first Undead Boss.
Don't shoot for whole six minutes and survive.
Use melee attack 100 times in one session.
Perform a rampage attack.