While the UFO is active it will deploy new PuPus to replace the fallen ones; this stage of battle is easy as using Cerberus Paradigm can kill them relatively quickly.
When the party destroys the UFO, the PuPus gain two abilities: Meteor and Rain down wayward stars! Both moves can easily dispatch an unprepared party, and so Protection (SEN/MED/SYN) and Combat Clinic (SEN/MED/MED) can help minimize damage. With an array of status enhancements and exceptionally high HP, the player should go with Aggression as Cerberus might not be able to cut down the initial number of PuPus and slightly charged chain gauge can help in quicker dispatch. Later, Cerberus can be used to deal with a smaller group.
PuPu is a reasonably good Medic. While it learns all of the major Medic spells, its true strength lies as a monster recruiter. With a good timing on the player's part, the Synchronization gauge can easily reach close to 999%.