Here is the full list of all 13 Dead Island Retro Revenge achievements.
FINISH A STAGE WITHOUT KILLING A SINGLE ENEMY
KILL 10 ENEMIES WITH ONE SLEDGEHAMMER POWER UP
FINISH A STAGE WITH THE CROSSHAIR OFF
FINISH A STAGE WITHOUT TAKING ANY DAMAGE
GET 20 PROJECTILE KILLS IN A SINGLE STAGE
COMPLETE YOUR FIRST LEVEL
ATTAIN 5 STARS ON ALL STORY STAGES
COMPLETE THE FINAL STAGE IN STORY MODE
COMPLETE MARATHON MODE
REACH WAVE 10 IN SURVIVOR MODE
REACH A COMBO OF 99 HITS IN ANY MODE
FINISH A LEVEL WITHOUT EVER CHANGING LANES
REACH STAGE 2-5 IN MARATHON MODE