Here is the full list of all 49 BULLET SOUL INFINITE BURST achievements.
Earned 25 and over medals in total
Shot down 25,000 units in total
Earned 25,000 coins in total
Earned Tamashii gauge 2,000 magnification in total
Earned Platinum Medal at stage 5 of Bancho mode
Earned Platinum Medal at stage 4 of Bancho mode
Earned Platinum Medal at stage 3 of Bancho mode
Clear stage 5 in Musou mode
Clear stage 4 in Musou mode
Clear stage 3 in Musou mode
Clear stage 2 in Musou mode
Clear stage 1 in Musou mode
Unlocked Musou mode
Watched a ending with Sadahl
Earned 50 HP items with your HP full in total
Watched a ending with Zenichi
Earn 500 various bonuses in total.
Collide against an enemy during a burst
Earned Platinum Medal at stage 2 of Bancho mode
Earned Platinum Medal at stage 1 of Bancho mode
Cleared a game without missing in caravan mode
Break my highest score in caravan mode
Watched a ending with Yun
Cleared stage 5 in normal mode
Cleared stage 4 in normal mode
Cleared stage 3 in normal mode
Cleared stage 2 in normal mode
Wawtched the ending with loop
Cleared stage 5 in burst mode
Earn 50 collection bonuses in total
Cleared stage 4 in burst mode
Cleared stage 3 in burst mode
Retried caravan mode
Cleared a game in caravan mode
Missed in caravan mode
Play a game to get in Turtle 10000
Cleared stage 1 in normal mode
Play a game to get in Red Hot Skull
Cancel a burst manually
Play a game to get in FA-98 Stinger
Cleared stage 2 in burst mode
Increased your coins' score rate up to 100,000 points
Used 2 bursts in a stage
Kept a burst for 30 seconds
Cleared stage 1 in burst mode
Beat a boss in a moment during a burst.
Used a burst
Recovered HP
Play a game to get in Piece of Cake