Here is the full list of all 22 Bebop and Tempo achievements.
Defeat Cadence for the first time.
You conquered your first castle!
Complete 1-8 with a score less than 26
Complete 2-9 without switching to Tempo.
Complete 3-2 only using Tempo.
Jump less than 4 times in 1-4
Complete 1-3 without attacking as Tempo
Complete Wave 10
Complete Wave 30
Complete 2-6 with a score less than 116
Complete 3-10 with a score less than 111
You completed all castles!
Defeat Cadence in Neo Beat City and get back to dancing!
Transform in Super Bebop
Dust yourself off and try again, it's only 100 deaths
You died 1,000 times...1,000 more wouldn't hurt
You have lived over 222 cat lives
You defeated Cadence for the first time as Swing and Dixie
You conquered your first castle as Swing and Dixie!
You dodged over 15 times in one level!
Reached 50% completion
Your training is complete...Now to challenge the world!