Here is the full list of all 34 Inside the Memories achievements.
Released the first memory
Released the second memory
Released the third memory
Released the fourth memory
Released the fifth memory
Released the sixth memory
Released the seventh memory
Released the eighth memory
Released the ninth memory
Released the tenth memory
Released the eleventh memory
Released the twelfth memory
Released the thirteenth memory
Released the fourteenth memory
Released the fifteenth memory
Released the sixteenth memory
Released the seventeenth memory
Released the eighteenth memory
Released the nineteenth memory
Released the twentieth memory
Finished the first level
Reached stage 19 without one single time's up
First time using a positive card effect
Used the shield thirty times
Achieved 3 gems in one level
Achieved all the memories
Got Game Over 20 times
Got negative card effect 30 times
5 memories unlocked
10 memories unlocked
15 memories unlocked
Achieved 15 gems
Achieved 40 gems
Achieved 55 gems