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