Big Meowth - Meow a lot.

For this achievement you will need to meow exactly 100 times.

You can just spam whatever button you use for "Meow/Bite/Pick up" (Default F for keyboard, X for controller) in between any mode and level and eventually you will get it.

Cat Taps - Turn on 5 faucets

This can easily be achieved by going into a level with a kitchen or bathroom and swiping your paws at the faucet handles. You will need to turn on 5 different faucets.

The "Mansion" level is a good pick for this achievement, as it has around 5 sinks.

Peak Purrformance - Run on a treadmill for 30 seconds.

This one is self explanatory, you will need to stay on a treadmill for 30 seconds. They have a chance of spawning in a Procedurally generated "Modern Home" and "Apartment" levels.