1 Their HP
The HP of the black Waltz is 250 and that of Sealion is 475.
2 Make sure you have enough potions
It would be very hard to win this battle without a stock of potions, preferably more than 5.
3 Attack the Black Waltz first
If you attacked Sealion the Black Waltz will quickly heal him. Keep attacking the Black Waltz first until you kill him so that you prevent him from healing Sealion.
4 Keep your HP above 100
As soon as your HP gets near 100 use a potion instead of attacking. Sealion can sometimes do a combo of more than one move and this can quickly drain your remaining HP. (See How to defeat Black Waltz no 3 – FF9 – Cargo Ship)
5 When the dot glows red
When the red dot on Sealion's body glows this means he might use his powerful Tsunami at any point. When that happens make sure you heal yourself very frequently. Keeping your HP above 120 is a good idea.
6 Use sword attacks
The best option you have in this case is using sword attacks unless you have learned the Tidal attack ability. (See How to defeat Black Waltz no 2 – FINAL FANTASY IX)
7 Use the Tidal attack ability
The Tidal attack ability can help you end this battle so fast. If you learned it use it instead of sword attacks.
8 Steal those items
The black Waltz has these items: Rmdy/SlkShrt, while Sealion has these: Ether/MythDgr.