The Red Tail is Faye Valentine's Zipcraft. It is unknown how she obtained it or the legalities of its acquisition. Adept at flying, Faye has stood her ground just as well as Spike has in aerial dogfights with her Red Tail.
When Faye first met the crew of The Bebop, they imprisoned her and planned to sell her ship. She, however, escaped in the Red Tail while Spike and Jet dealt with Gordon. Gordon double-crossed all of them, and Faye used her ship to reverse his rockets, destroying his ship. 
When the crew of The Bebop pursued Decker, Faye had found him and chased him, only to run into an explosive he was carrying. The ship was wrecked, forcing Jet to repair it. Later, Faye had to use the Red Tail to take one of his explosives to escape a mine. Faye had to use uncharacteristic care with the ship's robotic arms. 
When the crew of the Bebop went after pirates, Faye attempted to capture them with the Red Tail by playing dead until they picked up bait. However, the ship was hit with a virus, causing it to fire randomly and she was immobilized. It was fixed later, with a modification that the computer could be shut off in favor of a satellite-based navigation. It was not needed, however. 
- This ship may be named after the Redtail butterflyfish, a type of reef fish, or more likely the Redtailed Black Shark, which would fall into the same naming convention of the Swordfish II and the Hammer Head.
- It's also possible that this ship is called the Red Tail after the red-tailed hawk because it takes the form of a raptor: the pincers/guns are in the same position as a hawk's talons, slung underneath the ship, and the tail of the craft is red and similarly positioned to the red-tailed hawk's tail.