U will have to wait until you are lvl 30 then level up your Chouchou until he is lvl 20 and you will have a button labeled hatch under the picture of the egg the same goes with every other guardian beasts.
You should open the guardian beast tab and there you will find daily interactions that gives you guardian beast EXP. cards which you will feed to the guardian beast. The Basic guardian EXP card gives your beast 3000 exp. points. If you feed the guardian beast enough guardian EXP card he will gain lvl. At lvl 20 you will see a tab under the picture of the egg that says hatch. Click it an you will hatch the guardian beast.