Here is the full list of all 43 Rolling Gunner achievements.
Got all trophies
Stage 1 clear
Stage 2 clear
Stage 3 clear
Stage 4 clear
Clear stage 5
Clear stage 6
Novice mode clear
Casual mode clear
Clear original mode
Expert mode clear
Used power-ups
Used limiter release
Defeated the Bastalium Core
Obtained 1UP item
Raised the bonus counter to 10000
Clear Stage 1 with no mistakes
Clear Stage 2 with no mistakes
Clear Stage 3 with no mistakes
Clear Stage 4 with no mistakes
Clear Stage 5 with no mistakes
Clear Stage 6 with no mistakes
Game over in battle with Bastalium Core
Rolling gun made 100 laps
The limiter was released 20 times during one play.
Registered the score on the leaderboard
1st score extended
Second score extended
Reached a cumulative total of 1,000,000,000 points
Reached a cumulative total of 2,500,000,000 points
Reached a cumulative total of 5,000,000,000 points
Reached 100,000,000 points in one play
The limiter release was used at the maximum limit gauge
Maximized energy within 1.5 seconds after releasing the limiter
Challenged rank 50
I lost my ship without activating Auto Bomb
Cleared Stage 1 with no misses and no bombs
The boss activated the limiter release at the maximum limit gauge and did not hit until the end
Obtained an oversized score item
Obtained 100 or more oversized score items in the result
Obtained 100 oversized score items by releasing the limiter once.
Used the limiter release twice in stage 1
Used limiter release 3 times in stage 1