Here is the full list of all 16 Island Defense achievements.
Complete all levels on Hard Mode
Complete the game
Complete all levels with 3 stars
Level up all heroes to level 15
Upgrade Ice Tower to level 5
Upgrade all towers to level 5
Level up a hero to level 15
Upgrade Sniper to level 5
Upgrade Rocket Launcher to level 5
Upgrade Tesla to level 5
Upgrade Minigun to level 5
Upgrade Flame Squad to level 5
Unlock all Heros
Complete level with 3 stars on Hard Mode
Upgrade tower in the Laboratory
Complete level with 3 stars