Here is the full list of all 29 SAMURAI SHODOWN NEOGEO COLLECTION achievements.
Defeat the last boss Amakusa in Samurai Shodown
Defeat the last boss Mizuki in Samurai Shodown II
Defeat the last boss Zankuro in Samurai Shodown III
Get a Character Specific Ending in Samurai Shodown IV
Defeat the last boss Gaoh in Samurai Shodown V
Defeat the optional boss Mizuki in Samurai Shodown V Special or Perfect
Defeat the last boss Amakusa in Samurai Shodown as Haohmaru
Defeat the last boss Mizuki in Samurai Shodown II as Nakoruru
Defeat the last boss Zankuro in Samurai Shodown III as Shizumaru
Get a Character Specific Ending in Samurai Shodown IV as Kazuki or Sogetsu
Defeat the last boss Mizuki in Samurai Shodown II as Genjuro, Cham Cham, Neinhalt, or Nicotine
Defeat the last boss Zankuro in Samurai Shodown III as Shizumaru, Rimururu, Gaira, or Basara
Defeat the last boss Gaoh in Samurai Shodown V as Yoshitora, Yunfei, Mina, or Kusaregedo
Defeat the last boss Gaoh in Samurai Shodown V as Rera, Enja, Suija, or Rasetsumaru
Defeat Kuroko in Samurai Shodown II
Clear Samurai Shodown V as Poppy
Clear any game at its highest difficulty setting
Win a ‘Sword Clash’ in any game
Perform a ‘Barehanded Sword Grab’ in any game
Pick up an Item delivered by the Edo Express Delivery Man in Samurai Shodown or Samurai Shodown II
Perform a ‘Toy Transformation’ move in Samurai Shodown II
Eviscerate your opponent at the end of a match in one of the first three games
Perform a 'Weapon Breaking Technique' or 'Weapon Flipping Technique'
Perform a 'No Contest' in Samurai Shodown IV
Perform a 'Link Slash' move in Samurai Shodown IV
Perform a 'Fatal Flash' move in Samurai Shodown IV, Samurai Shodown V, Samurai Shodown V Special, or Perfect
Perform a 'Honorable Death' move in Samurai Shodown IV, Samurai Shodown V, Samurai Shodown V Special, or Perfect
Perform an 'Overkill' move in Samurai Shodown V Special or Perfect
Defeat the optional boss Mizuki in Samurai Shodown V Special or Perfect as Amakusa, Zankuro, Gaoh, or Mizuki.