After your pet reaches a certain level, your pet will automatically learn a random skill. If your pet is at or above Lv50 and has 1,000 affinity, it will automatically get a skill. If your pet is at or above Lv75, your pet can learn a skill without requiring 1,000 affinity. Skills can be randomly reset for 500 island points. Pets can learn duplicate skills. The skills below that have stars next to them can only be obtained if your pet is a boss or god pet (only available from the Item Shop). Skills learned are random with no known correlation to your pet's stats or what you feed it.
Read more: http://iruna-online.proboards.com/thread/46/pet-skills#ixzz3teoWSE1H