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