Here is the full list of all 24 Ninja Shodown achievements.
PERFORM A 5 HIT COMBO IN ARCADE MODE
REVIVE AN ALLY IN ARCADE MODE
COMPLETE TEMPLE ZONE IN ARCADE MODE
COMPLETE DOJO ZONE IN ARCADE MODE
COMPLETE DOWNTOWN ZONE IN ARCADE MODE
COMPLETE MUSEUM ZONE IN ARCADE MODE
COMPLETE AREA 88 ZONE IN ARCADE MODE
DESTROY BOSS AT THE END OF ARCADE MODE
ACHIEVE QUICK ROUND BONUS IN EVERY ROUND OF A ZONE IN A SINGLE ARCADE MODE GAME
ACHIEVE RANK S IN EVERY ROUND OF A ZONE IN A SINGLE ARCADE MODE GAME
COMPLETE ARCADE MODE IN UNDER 20 MINUTES
SCORE 250,000 POINTS IN ARCADE MODE
SCORE 500,000 POINTS IN ARCADE MODE
SCORE 1,000,000 POINTS IN ARCADE MODE
KILL 100 ENEMIES IN A SINGLE ARCADE MODE GAME
KILL 500 ENEMIES IN A SINGLE ARCADE MODE GAME
PERFORM 25 CRITICAL KILLS IN A SINGLE ARCADE MODE GAME
PERFORM 50 CRITICAL KILLS IN A SINGLE ARCADE MODE GAME
PERFORM A 10 HIT COMBO IN ARCADE MODE
PERFORM A 20 HIT COMBO IN ARCADE MODE
PERFORM 25 PILEDRIVER KILLS IN A SINGLE ARCADE MODE GAME
PERFORM 50 PILEDRIVER KILLS IN A SINGLE ARCADE MODE GAME
USE A BARREL TO KILL AN ENEMY IN THE DOWNTOWN ZONE OF ARCADE MODE
KILL AN ENEMY FROM A SHURIKEN DEFLECTION IN ARCADE MODE