Sin's Left Fin is a boss in Final Fantasy X. This battle takes place during the fight to get inside Sin, and is the first of a series of boss fights. Like the battle against Evrae, the player is on the Fahrenheit and can fly in and out of range of physical attacks.
Flying in and out of range of Sin changes its physical attack between a heavily delaying ram or a long-ranged smack, which can deal over 1000 damage to the party. Sin can randomly use Negation after being targeted, which simultaneously removes Armor Break and Mental Break from it and any status buffs from the party, except Auto-Life. When the fin's core starts charging, it will use Gravija on its next turn, which drains 75% of the party's current HP if up close. The core gathers energy after three regular actions, but not while far away.
Whether Sin uses its physical attack or skips its turn is determined by how many times the party has attacked it since it last took action. While up close, the fin has a 33% chance to attack, which increases to 66% after being attacked once, and 100% after two attacks. At a distance, it requires seven hits to trigger an attack. After the fin attacks, the counter resets. Battling up close and at a distance run on the same counter, the former simply having lower requirements. When attacking with an aeon, it is counted as two attacks.
Negation also has a counter determining its use while fighting up close. It starts at 2 and increases by 2 for the first break inflicted on Sin; 1 for the second break; 1 for each instance of Shell, Reflect, and Haste on the party; 1 if Protect is on the rightmost party member; and 2 if Protect is on the leftmost party member. 3 is subtracted from the sum total, which is then divided by 16, thus becoming the chance of Negation being used. While far away, Negation merely has an 80% chance to be used and only when Sin is afflicted with Mental Break, and it will not target the party.
There are two unused abilities for the battle that would allow Sin to draw near or pull away from the Fahrenheit of its own volition.
Because Sin's attacks are scarcer and less intimidating while far away, the fight is made simpler when fighting at a distance. Inflicting Armor Break and pulling back allows Wakka's attack to whittle away Sin's HP, while Hastega, Protect, and Cheer can be used to buff the party. When fighting up close, it's safe to cast Protect on the central party member and either cast Haste on one party member or use Armor Break on Sin. Piercing weapons can be used to effectively damage Sin without Armor Break.