Here is the full list of all 10 Battleships: Command of the Sea achievements.
Sink the first enemy carrier
Win the battle as US forces
Win the battle as Japanese forces
Win the battle as every US Admiral
Win the battle as every Japanese Admiral
Play a game in multiplayer mode
Use all the Japanese faction skills at least once
Use all the US faction skills at least once
Use the Admiral ability
Lose without destroying a single enemy ship