Here is the full list of all 21 Touhou Mystery Reel achievements.
Defeating Motoori Kosuzu
Help little fairy
Complete Sakuya's challenge
Defeat Reimu
Open the game at least once
Make Motoori Kosuzu step on the banana
Complete Flandre's rehearsal
Clear stage 1 and complete the mission
Some things should not be done
Completely defeat Motoori Kosuzu
Gain friendliness of the fortune cat
Make the chicken soup
Clear Youmu's training
Perfectly counter Reimu's aerial attacks several times
Get the last hit of Reimu immediately after she falls