Here is the full list of all 38 Starship Inspector achievements.
Hit an enemy ship for the first time
Recieve hull damage for the first time
Begin your adventure
Complete tutorial
Talk to Solomon at one of the Trade Stations
Complete 5 sectors using Devastator Frigate on medium difficulty
Defeat Goliath Dreadnought using Ferocious Battleship on hard difficulty
Earn 10,800 points using any Devastator Starship
Arrive at Sector Eight using any Devastator Starship and without ever changing its starting weapons on medium difficulty
Defeat the Summoner using Gladius Cargo Corvette on medium difficulty
Complete 5 sectors using Independence Medical Corvette on medium difficulty
Complete the Fallen Judge campaign
Reach Sector Eight using Judgment Dreadnought on hard difficulty
Spare 60 enemies when they beg for mercy
Have mercy on your enemy 52 times and help creatures in distress 56 times
Earn 10,800 points using any Harmonian vessel
Upgrade all systems to the maximum on Eveningstar Battle Cruiser before reaching Sector Eight
Complete 5 sectors using Paradise Dreadnought on medium difficulty
Reach Sector Eight using Nirvana Escort Corvette on hard difficulty
Destroy an entire Bugzer crew by using poison
Reach Sector 7 using Tacca Frigate
Install all systems on Cordyceps Battle Cruiser before reaching Sector 6
Earn 10,800 points using any Bugzer vessel
Assemble a Bugzer-only crew using Dionaea Dreadnought before reaching Sector 3
Make a purchase at each of 22 Trade Stations before reaching Sector Eight
Purchase and sell something at each of 22 Trade Stations before reaching Sector Eight
Earn 11,008 points while using any Trade Federation starship
Reach Sector 7 without visiting any Trade Stations at all
Earn 10,800 credits
Obtain Blackbeard's codex
Start your encounter on any Pirate Starship with 1 hull point and survive through the battle
While being on any Pirate Starship, board Tortuga Battle Island and defeat it from within not using long distance attacks at all
Defeat 2 enemies simultaneously and survive while using Imaginarium Cruiser
Earn 9000 points using any Pirate Starship
Arrive at Sector 6 without losing any of your crew members
Talk to the bartender.
Defeat Varmage Kzohlu.
Complete "The Great Secret" campaign.