Here is the full list of all 37 Her Majestys Ship achievements.
Reach Commodore rank for the first time
Reach Rear Admiral rank for the first time
Reach Vice Admiral rank for the first time
Reach Admiral rank for the first time
Reach Admiral of the Fleet rank for the first time
Build 5 forts in one game
Have 3 ships in your squadron
Destroy 5 pirate ships in one game
Be in a war with dutch
Win a game while having all Dutch ports captured
Win a game without fighting with other player ships
Finish your first Admiralty Order
Play your first multiplayer session
Play 1 multiplayer game with your friend
Capture your first fort
Have one sailor to reach max rank
Plunder one shipwreck
Destroy enemy trade ship for the first time
Recruit your first officer
Buy 100 Captain Points in one game
WIn 5 multiplayer games
Finish your first event
Heal sick sailor
Recruit 5 sailors in tavern in one game
Spend 25 Gold in shop in one game
Destroy all other nations main ships three times while playing with more than 1 Ai player in the game in endless mode
Sink one nation's main ship three times in endless mode
Have 3 Additional ships in play for 30 minutes in endless mode
Capture all Dutch ports in endless mode
Build more than 10 Forts in endless mode
Play for 60 minutes without sinking and mutiny on Admiral difficulty in endless mode
Defeat three Dutch warships in endless mode
Sail over 1000 sea miles in endless mode
Complete 100 admiralty orders in endless mode
Complete 100 event orders in endless mode
Promote 5 Officers to their own ships in endless mode
Train 25 Marines in endless mode