Beatrix appears three times as a boss in Final Fantasy IX. Beatrix is massively powerful, having many strong attacks, and can heal herself with White Magic. The game is fixed so that Beatrix does not fall in battle even when her HP is supposedly depleted.
The party has no choice but to stay alive until Beatrix uses an unblockable finishing move that instantly knocks everyone down to 1 HP; either Stock Break or Climhazzard. She uses this when her HP hits 0 or after getting ten turns. She also uses the Shock attack to do massive damage to a single party member, usually KOing them. If the party is defeated before this, it will be a Game Over.
Beatrix can be stolen from and has many good items to steal, although it is difficult to get all the items before she finishes the battle. If the player is not concerned about this, and Quina is in the party (optional for the first and second battles, impossible for the third), they can KO Quina before the battle, save, use a Phoenix Down on him/her and reset until the Phoenix Down restores exactly 1 of Quina's HP, and then have Quina open the battle with Limit Glove, which will defeat Beatrix and force her to use Stock Break. In the second battle, having Quina cast Auto-Life on him/herself can emulate this effect.