Cloud: I couldn't finish 'em. Looks like this's gonna get complicated.
The following tables are incomplete and require the specify if an attack sets HP to one, or does damage to lower HP to one. entries to be filled. If you wish, please examine the table and add anything missing. Remove this notice upon completion.
HP to one abilities reduce the target's HP of one regardless of their current HP. This is sometimes done by simply setting the targets to one HP, at other times by inflicting damage to them equal to their max HP minus one. They are commonly used by final bosses and superbosses. One of the best known of these abilities is Heartless Angel, which has become the trademark attack of Sephiroth.
Omega Weapon has a similar ability called Megiddo Flame. The ability does not reduce the party to one HP, but deals a guaranteed 9,998 damage to the entire party, and thus the only way to survive is to have 9,999 HP, leaving the party with one HP after the attack hits.
Diving into the game code reveals two dummied spells specific to Selphie, Percent (a reduce-HP-to-1 move similar to Matra Magic), and Catastrophe (major damage to all enemies). These two spells were removed from Selphie's spell list in the final build of Final Fantasy VIII, but can be found via third-party data exploitation programs, although they just use Fire's spell animation.
Beatrix uses Stock Break and Climhazzard to reduce the party's HP to 1 when fought as a boss, and these abilities cannot be blocked or avoided. This ends the battle. When these abilities are used by the player's party, Stock Break and Climhazzard instead simply deal major non-elemental damage to all enemies.
There are no enemy attacks that bring the party's HP to one HP, but in the Zodiac versions, Judge Ghis, when fought on the final Trial Mode challenge, uses Elixirs on reversed party members leaving them with 1 HP.
Shango uses Divine Storm to reduce the party's HP to 1 when fought for the first time. This leads to the end of battle once he has used it. The same goes for Glacial Dance used by Cocytus. The battle are scripted events when these are used. When these abilities are later used by them during their real battle, they deal normal damage.