There is an art to animal training, example:
Nightmare (default : magery/dragon breath) = (lvl 2>3) learn poisoning, can also learn poison breath/aura of nasua, train to GM (lvl 3>4) switch back to Magery (not maining poisioning means no poison melee attacks but the pet can still perform skills and a pet with magery can use the poisoning). Alternatively you can train the pet skills and switch magic abilities at stage 5, some pets jump in slots if they are given extra skill points and this is especially true if you get ninjitsu/bushido skills for free through bladeweave use.
The Cu Sidhe can learn a special ability and a special move + magic ability, must be done in this order if you weren't aware. Giant Beetle/Fire Beetle's are also mountable pets that can be trained with poisioning but for poison attacks to be lvl 5 they must be given at least 1 poison ability and as for now only tamable creatures who have poison by default can auto attack lethal poison.