Here is the method about fight together with your pey in Boi.

To fight with your pet, first you must summon him. You can do this via the Pet Tab by selecting the Pet, and then selecting the Summon button.

Then, you're free to go out and fight monsters to your heart's content. The Rainbow Valley is a special area designed for pets. To gain access, you must speak to Ludia in Atlantis Square (Location 99,194).

Select Teleport, and then select to go to Rainbow Valley. In Rainbow Valley, you will find many Boi Gold that are designed to yield interesting pet opportunities. Additionaly, it is also the location of the NPC Gadro. Gadro will allow you to Meld and Boost your pets.

Pet Boost:
Speaking to Gadro will allow you to choose Pet Boost. Boosting your pet will require a Magic Stone of Growth, which can be found in Dragon Island during the corresponding event. You can also use a Catalyst of Growth, found in the Marketplace, to increase the rate of successful Boosting. After a successful Boost, your pet's Growth stat will increase.

Another way to Boost a pet, is to use another pet instead of boi money. To do this, select Pet instead of the default selection of items:

This will bring up the Pet Boosting UI. For the Boost to be successful, the Auxiliary Pet must have a higher Summon Level than the Target Pet. Note that the Essence Level of the Auxiliary Pet must be above 0, while the Target Pet's essence may remain 0.