Here is the full list of all 28 Skull Island: Rise of Kong achievements.
Become the King of Skull Island
Defeat your nemesis to avenge your parents
Make Kong the best fighter by unlocking all his skills
Reach Kong's potential by obtaining all skillpoints.
Collect all the collectibles in Skull Island
Complete all the ascension challenges of Skull Island
Kill a boss without losing health
Defeat Gaw without using special abilities
Defeat the monster that awakened you
Defeat the big fighter that inhabits Stage 2
Defeat that annoying group of deathrunners
Defeat the dark creature obstructing the caves of Stage 4
Kill a boss without using special abilities
Kill 5 enemies in less than 10 seconds
Kill a creature with another creature
Kill 250 enemies
Kill all types of Creatures in Skull Island
Execute 10 Creatures
Explore all of Stage 1
Explore all of Stage 2
Explore all of Stage 3
Explore all of Stage 4
Explore all of Stage 5
Kill 100 enemies
Complete the tutorial
Find your first collectible
Kill a flying enemy with a rock