Defeat the Saucy Pirate is a mission in The Lost Frontier, and is a means to the mission Search Far Drop for seeker piece. After discovering that the eco seeker needed three coordinate spheres before it could function, Keira determined one was near Far Drop.
Upon arrival, Jak met with Barter who pointed out the Saucy Pirate, who was in possession of one of the spheres (referred to as a "Precursor rune sphere" by Barter). Barter stated he felt Jak could "persuade" her to give it up, and while Jak was prepared to offer her cash, the pirate female decided she would wager it in a brawl (requiring Daxter as Jak's wager for a "fur coat"). Jak agreed, to Daxter's vexation.
Beware of the Saucy Pirate, as she looks like a standard human, but possesses health and speed far superior to Jak. To counter her speed you must use eco reflexes, ideally as much as possible, which allows you to dish out damage for a short time without fear of repercussion or dodge her attacks. Though you can also use the eco shield, if available, in a pinch to ignore her attacks entirely.
The first part of the fight consist of the Saucy Pirate charging towards you, sometimes with a quick dash, while trying to hit you with her scimitar. It is possible to cause her to flinch and stop moving for a second with a direct punch, though this will not work if she is swinging her blade. After enough damage has been dealt she temporarily retreats, at which point her allies attack you. Kill all the attacking pirates, after which the Saucy Pirate will start to either throw bombs on the tavern floor, or jump on one of the tables and begin shooting her blaster at you. In case of the former, simply dodge the reticles on the floor to avoid the bombs. In case of the latter, which she will proceed to do regardless of whether she throws bombs or not, use eco reflexes to close in on her and destroy her table, note that it is also possible to destroy all tables beforehand to avoid this phase entirely.
Now she will repeat the first part, in which she solely uses melee, followed by the temporary retreat and the surge of pirates coming to her aid. As before, she now will follow up with throwing bombs and then using the tables, if they are still standing, as a platform to fire at you. Once her health has been pummeled low enough she will retreat one more time and throw a new type of bomb in the center of the room. This bomb emits four laser beams and then starts rapidly spinning around, before detonating after five seconds to release a shockwave of flame. She will follow up with another identical bomb ans although they are potentially quite deadly, they can be avoided and ignored entirely if you are standing on the stage below the ledge on which she is standing, as this area is slightly too high for the bombs to reach. After the bombs, she will jump down once more after which you can proceed to finally defeat her.