Here is the full list of all 22 Sea Battle: Through the Ages achievements.
Sink down 50 ships
Sink down 100 ships
Sink down 200 ships
Sink down 2 ships in a row
Sink down 3 ships in a row
Save 50% of your fleet
Save 70% of your fleet
Sink down a four-decker without a single miss
Win a battle with a single ship remaining
Successfully strike a target 3 times in a row
Successfully strike a target 4 times in a row
Successfully strike a target 5 times in a row
Hit a target with the first shoot of the round
Participate in 10 battles
Participate in 20 battles
Participate in 30 battles
Achieve 3 victories in a row
Achieve 5 victories in a row
Achieve 7 victories in a row
Visit the game 3 days in a row
Visit the game 5 days in a row
Visit the game 10 days in a row