The lost cats are cameo (or cameow) NPCs with a small bit of dialogue that you can find along your climb, unique from the shopowners. There are 24 of them in total to find for the achievement.

I will go through them in order. Should go without saying but spoilers inbound!

The City contains 4 cats.

1. Skybilz
Found in an alcove to the left of the green yarn ball as you follow the main path.


2. cjya
Found next to the fountain in the middle of the city.


3. Kiara
On the backside of the yellow building after following the path of some wooden boards.


4. Andy
Found on the outside of Cousin Tabby's Cat Cafe.

The Ascent contains 3 wandering cats.

5. authorblues
On the side of a red building after some tables.


6. Gordon
Found on the building straight forwards from the bed memory.


7. Loaf
Found hidden on a building to the right of the bed memory.

The Aquarium contains 5 wandering cats.

8. NobletOfU
Found on a side path before jumping down to the first ship. This one is very tricky, requiring you to launch yourself with a cannon shot in order to make the jump to the island.


9. JustKitt
Found along the main path, right before a tree-branch jump.


10. SmallAnt
After being shot from the cannon, drop down the hole in the island you land on. There will be another cannon there to return to the first island, and SmallAnt will be found next to that cannon.


11. Billy
Found hidden behind a waterfall in a spinning barrel section.


12. Spikevegeta
Another tricky one to find. After taking the second fish ride, right outside of the next cafe, drop down and wall run to the left of the entrance to the area. A bit higher up along the outside of that island you will find Spikevegeta.

The Trip contains 4 cats.

13. PangaeaPanga
Found on the lowest windmill island. Can be jumped down to from above near the first rock amplifier.


14. Vswed
Found on an island near the main path, right before the first coffin.


15. FoxieKat
Found behind a waterfall on an island below the final windmill section of the level.


16. ParkenHarbor
Found in a secret passage under the well in the final village at the top of the level. Requires a bit of platforming to get to.

The Amphitheater contains 4 cats.

17. Kinn
Found along the main path on the bridge with two records.


18. Starr0Chris
Found along the main path, overlooking the main stage.


19. HKayPlay
Found to the side of the main path, next to a bunch of speakers on the island with a giant pretzel.


20. Aurateur
Found on the very top of the stage.

The Lasers contains 4 cats.

21. Wavy
Found after taking an extra trip around the second rotating vertical wall section.


22. BarbarousKing
In section 2, after the second section with the green platforms that go up and down, take the path following the yellow blocks that appear and disappear. This takes you to a rotating platform section. BarbarousKing is on top of one of the blocks in that section.


23. LilAggy
From the island with the memory, take the lower path along a rotating block section.


24. CraftyBoss
During the final wallrun section of the level, there is a secret path on the other side of one of the walls, shown above. CraftyBoss is on the top of one of the pillars on the islands found on this path.