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