Here is the full list of all 21 Fleet Star V achievements.
Cause 10,000 points of damage against enemy ships in all attended battles.
Destroy 1,000 enemy compartments in all attended battles.
Personally lead your fleets to victory 10 times.
Personally lead your fleets to victory 50 times.
Personally lead your fleets to victory 100 times.
Claim your first victory against the enemy.
Claim the enemy's location as yours.
Capture 10 enemy locations.
Capture 50 enemy locations.
Capture 100 enemy locations.
At the start of a cycle, have one million material.
Win a storm battle type.
Capture 5 enemy ships in a single battle.
Personally capture 100 enemy ships.
During battle, have a Captain sustain a critical injury or die.
Promote 10 crew members to officer positions (Captain, Navigator, Ship's Doctor or Chief Engineer).
Our men are running from the battlefield! Shameful display!
Heal your crew for 100,000 points across all campaigns.
Repair your ships for 100,000 points across all campaigns.
Win a campaign (including campaigns created in the Campaign Builder tool).
Complete the tutorial.