The King of Fighters '98: The Slugfest Hints & Cheats

Press a button immediately after beating the opponent. Each button gives a different winning pose.

When you have to select the order of the characters, first hold START and a face will appear on each character. The colour of the face shows whether the power stocks will be conserved or whether you'll lose all of them when you control the next character.
White normal face: the power stocks will get passed on
Yellow smiling face: the power stocks will get passed on and you'll get one more too
Red angry face: you'll lose all the power stocks
You may then set up your team depending on how your characters are feeling.

When your fighter is being held, quickly tap ABC to have an unused teammamte jump in and free that character. Obviously, this doesn't work if all your teammates have already been defeated.