Relics are some kinds of hidden mission if you play exactly as they planned in some levels.
The Relic can be seen at the exit gate (not all levels have it).
For example: some levels do not need the cat to use the skill. If you do not use it, the relic can be collected when the level is clear.
Here are all Relics lists in Timelie game.
ch.2—————————-
-4 Don’t fix bridge.
-5 Speed run.
-6 No meow!
-8 No meow!
ch.3 —————————
-3 Don’t let them see you.
-6 No kill.
-8 No meow!
-10 Speed run.
-11 Speed run.
-12 Speed run.
-13 No kill.
ch.4—————————
-4 No kill.
ch.5—————————
-1 No kill.
-2 Get 1 meow!
-3 No kill.
Credit to Kosakk