Reply 14# prophecy0000's post
If you're asking about the skill slots which, depending upon the type of pet, will enable the pet to learn a different type of attack or "move", then there is no specific level at which the skill slot will be unlocked. Unlocking skill slots purely depends upon the growth rate & the spirit of the pet. The higher the growth rate & spirit of the pet, the faster the skill slot opens.
The other way a pet can "learn more moves" is by taking a look at the skills tree. The more training points a pet has, the faster you can max out a skill in the tree. This will, again depending upon the type of pet, enable the pet to gain a new "move".