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