Here is the full list of all 13 Dead Island Retro Revenge! trophies - there are 9 bronze, 3 silver and 1 gold.
Kill 10 enemies with one sledgehammer power-up
Complete your first level
Finish a stage without taking any damage
Attain 5 stars on all SP levels
Complete the Final Stage in Story Mode
Complete Marathon Mode
Reach Wave 10 in Survivor Mode
Reach a combo of 99 kills in any mode
Finish a stage without killing a single enemy
Finish a stage without ever changing lanes
Get 20 projectile kills in a single stage
Reach Stage 2-5 in Marathon Mode
Finish a stage with the crosshair off