Here is the full list of all 40 ILY achievements.
Complete level 1
Complete level 2
Complete level 3
Complete level 4
Complete level 5
Complete level 6
Complete level 7
Complete level 8
Complete level 9
Complete level 10
Complete level 11
Complete level 12
Complete level 13
Complete level 14
Complete level 15
Complete level 16
Complete level 17
Complete level 18
Complete level 19
Complete level 20
Complete level 21
Complete level 22
Complete level 23
Complete level 24
Complete level 25
Complete level 26
Complete level 27
Complete level 28
Complete level 29
Complete level 30
Complete level 31
Complete level 32
Complete level 33
Complete level 34
Complete level 35
Complete level 36
Complete level 37
Complete level 38
Complete level 39
Complete level 40