While Beatrix’s hp is 4700 you only need to let her lose a fraction of that HP for the fight to end as she will stop the fight and leave after losing some of her HP.
The battle is easier with Quina
Beating this battle is easier if you have Quina in your party, however it can still be beaten without her. In case you have Quina use her for healing every turn.
Use Freya’s lancer ability
Freya’s lancer ability causes a lot of damage and also steals MP from enemies. Keep using it until you run out of MP then start jumping.
Equip coral ring
One of the powerful attacks for Beatrix is the thunder slash. The damage of this attack can be greatly reduced if you used an item that can absorb thunder attacks such as the coral ring.
Use Quina’s mighty guard
If you have Quina in your party then let her use her mighty guard to protect the party from Beatrix’s attacks and to reduce their effectiveness.
Shock wave can kill instantly
Beatrix’s attack shock wave deals around 800 damage to a single character. At this point it would be hard to have a bigger HP and so this attack will usually kill a player instantly.
Let all party stand in the rear line
To reduce the power of the attacks let all your party stand in the rear row. If you have Equipment that protects against thunder then you can move Zidane and Freya to the front line since they will be the one attacking Beatrix. (See How To Win Final Fantasy 9 Card Game)
Use Freya’s Reis’ wind
Using Freya’s Reis’ wind ability can help a lot since it will allow you to Regen your HP.
Turn offensive when she cures herself
When Beatrix cures herself know that the battle is about to end. Stop curing and let all party members become offensive.
The fight has a time limit
Many players believe that this battle has a time limit and that your goal should just be surviving until that invisible timer runs out.
Stock break is the last attack
When Beatrix casts stock break, which reduces the HP to 1, then know that the battle is over. (See How to defeat Scarlet Hair in Final Fantasy 9?)
How to defeat Beatrix in Cleyra in Final Final 9
How do you beat Beatrix in Final Final 9? Final Fantasy IX: Beatrix in Cleyra (Boss Battle)