is there a way to make a beasts intellegence raise ?

Yes,you can do it by using Nutpeas.Nutpea is a magic fruit that can be bought from the Premium Shop,found on the islands during exploring or traded by other users.

The other (and probably cheaper) way to do it would be by changing the pet's diet. On the left side of your pet's page, there's a box with some green stars in it. That is the pet's diet composition. If you hover over the question mark in the corner, you can see what food type affects which stat. Feeding a pet more or less of each food influences the chances of each stat gaining points when the pet levels up.

Simple version: feed it more animal carbohydrates. ^^ Its intelligence will then have a greater chance to increase as it levels up.

Oh,I forgot about this.

The magic fruits are usually for when you urgently need a pet with specific status points for quests or different activities and you don't have enough time to train them.

Or it's already at level 50 and you need its stats to rise still further...