Its Nausea Powder is not too threatening as long as there is an Alchemist with the Remedy ability or several Antidotes in stock. It's much more difficult when Oversouled, since it has access to the powerful Flare spell.
After the player unlocks the Cactuar Hollow in Chapter 5, they can recruit the Big Bully Cap to their party with a Trap pod M or Trap pod SP targeting the Fungus species in Bikanel.
Big Bully Cap comes into the party having learned Waterga, Nausea Powder, and White Wind. Unlike an enemy Big Bully Cap, the recruited version does not have an immunity to any status ailment, so giving it the Mascot dressphere or the Abominable Garment Grid is highly recommended. Big Bully Cap learns Stonetouch, Poisontouch, Sleeptouch, and Silencetouch after being hit by a status ailment-inducing attack (e.g. Bad Breath) and surviving it.
Fiend Tale Edit
A notable Big Bully Cap dreamed of becoming a singer before she died during an attack by Sin. After watching Yuna's concert, Big Bully Cap decided to act on her dream with Barkeep as her voice coach. Eventually, Big Bully Cap holds her private concert, but the Fiends attending died from hearing her sing. Believing she did a good job, Big Bully Cap jumped off the airship to find another venue.