It uses Earthquake to damage the whole party at once. It is very difficult to steal the Fairy Flute from him. Even with Bandit equipped each steal attempt only has a 1/256 chance of success. It otherwise cannot be obtained until much later.
Casting Float on everyone protects the party from Earthquake. Zidane should steal while Vivi casts Slow or focuses. Dagger/Eiko can heal and cast Float, targeted on the entire party each turn. It should be renewed every couple of turns, or else the party may be caught in Hilgigars's Earthquake attack.
Once Zidane has stolen enough items from Hilgigars Vivi should cast Bio, Dagger summonRamuh, and Eiko summon Fenrir, healing when necessary.
Hilgigars comes from "hill gigas". [view·edit·purge]Gigas is a popular term for races of giants in fantasy games. Gigas is a Greek word meaning "giant," originally used to describe the race of Gigantes in Greek mythology and is used in the scientific name, as the specific epithet, of hundreds of species of animals and dozens of plant species to denote their size.