To tame a pet, a Cute Pet Taming Item must be used. These items are obtained through monster drops or special quests, you can also get it from exchanging Colorful Shell that can be bought via BIG CAT COINS.  To use one, Go to the monster you want to be a pet. Once you are near,  an Option will pop-up in the screen asking to use the item and will ask you if you want to catch the desired pet. A slot machine will appear and it must be clicked to get a chance at taming the monster. In case of failure, the taming item is lost and no pet is gotten. In case of success, the taming item will be used and a Pet Egg will be received.

If you want to know how to have a 100% catch rate, Please check this guide.
Ragnarok M: Eternal Love – Trick on how to have a 100% catch rate in taming a pet.

Learn more about Colorful Shell.

Taming item for Lunatic

The Slot Machine

Pet Successfully Captured!