Here is the full list of all 29 King of Seas achievements.
Boost a settlement completely
Earn 500.000 gold
Find 5 sunken treasures
Complete the world's map for the first time
Conquer 5 enemy settlements
Sink 50 ships
Earn 100.000 gold from trade
Sink 10 ships
Commerce every kind of resource for the first time
Earn 10.000 gold from trade
Earn 1.000 gold from trade
Complete your first game
Complete the game in Ship's boy difficulty
Complete the game in Gunner difficulty
Complete the game in Captain difficulty
Complete the game in Corsair difficulty
Complete the game in King of Seas difficulty
Complete 30 side quests
Reach the maximum level
Find 10 sunken treasures
Find 30 sunken treasures
Sink 100 ships
Sink all Sovereign Pirates
Conquer 10 enemy settlements
Conquer 30 enemy settlements
Fish successfully 10 times
Fish successfully 30 times
Fish successfully 50 times
Find every kind of fish for the first time