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