Here is the full list of all 32 Captain Firehawk and the Laser Love Situation achievements.
Earned 15 stars
Stage 6 Clear
Killed over 2000 enemies
Killed the crab
Earned 10 stars
Stage 5 Clear
Killed 1500 enemies
Stage 4 Clear
Held over 1500 coins
Held over 1000 coins
Killed over 1000 enemies
Earned 5 stars
Stage 3 Clear
Earned 2 stars in a single stage
Earned 3 stars
Stage 2 Clear
Earned 3 stars in a single stage
Held over 500 coins
Held over 200 coins
Earned one star
Stage 1 Clear
Killed over 300 enemies
Stage 0 Clear
First Dead Enemy
Fist Impact Received
Earned 18 stars
Failed due to poverty
Failed because the giantess wasn't ready
100% in one stage
100% in 3 stages
100% in all stages
Killed over 3000 enemies