Here is the full list of all 12 The King of Fighters '98 Ultimate Match Final Edition achievements.
Achieve 100 wins in online fight.
Achieve 10 straight wins in online fight.
Achieve 50 wins in online fight.
Iori(Ura) or Leona(Ura) appear as CPU ( Arcade/Single Play Only ).
Perform an assist attack ( Arcade Play Only ).
Achieve 5 straight wins in online fight.
Achieve 10 wins in online fight.
Finish the game ( can't lose one round, can't continue) ( Arcade/Single Play Only ).
Highest point exceeds 300 thousand ( Arcade/Single Play Only ).
Pass level perfectly in one round (without injury) ( Arcade/Single Play Only ).
Finish the game (can continue) ( Arcade/Single Play Only ).
Achieve straight win ( Arcade Play Only ).