Here is the full list of all 19 Puzzle Bobble2X/BUST-A-MOVE2 Arcade Edition & Puzzle Bobble3/BUST-A-MOVE3 S-Trib achievements.
Get an "Excellent" rank in Challenge Mode
Get a "Good" rank in Challenge Mode
Get an "Average" rank in Challenge Mode
Complete Round 6 in Puzzle alone
Complete Round 5 in Puzzle alone
Complete Round 4 in Puzzle alone
Complete Round 3 in Puzzle alone
Complete Round 2 in Puzzle alone
Complete Round 1 in Puzzle alone
Score over 3 000 000 points
Score over 5 000 000 points