Here is the full list of all 48 Castlevania Advance Collection achievements. It takes around 40-50 hours to unlock all of the achievements on Windows.
Defeat Cerberus -- Circle of the Moon
Defeat Chaos -- Aria of Sorrow
Defeat Julius -- Aria of Sorrow
Defeat Graham -- Aria of Sorrow
Defeat Balore -- Aria of Sorrow
Defeat Legion -- Aria of Sorrow
Defeat Death -- Aria of Sorrow
Defeat the Headhunter -- Aria of Sorrow
Defeat the Big Golem -- Aria of Sorrow
Defeat the Great Armor -- Aria of Sorrow
Defeat the Manticore -- Aria of Sorrow
Defeat the Creaking Skull -- Aria of Sorrow
Defeat the Necromancer -- Circle of the Moon
Defeat the Iron Golem -- Circle of the Moon
Defeat Adramelech -- Circle of the Moon
Defeat the Dragon Zombies -- Circle of the Moon
Defeat Death -- Circle of the Moon
Defeat Carmilla -- Circle of the Moon
Defeat Hugh Baldwin -- Circle of the Moon
Watch the ending -- Circle of the Moon
Watch the ending in Magician Mode -- Circle of the Moon
Nathan collects all the cards -- Circle of the Moon
Defeat the Giant Bat -- Harmony of Dissonance
Defeat the Living Armor -- Harmony of Dissonance
Defeat the Skull Knight -- Harmony of Dissonance
Defeat the Minotaur -- Harmony of Dissonance
Defeat the Golem -- Harmony of Dissonance
Defeat the Devil -- Harmony of Dissonance
Defeat the Giant Merman -- Harmony of Dissonance
Defeat the Max Slimer -- Harmony of Dissonance
Defeat Peeping Big -- Harmony of Dissonance
Defeat Legion (saint) -- Harmony of Dissonance
Defeat Shadow -- Harmony of Dissonance
Defeat Pazuzu -- Harmony of Dissonance
Defeat the Minotaur Lv2 -- Harmony of Dissonance
Defeat Legion (corpse) -- Harmony of Dissonance
Defeat Death -- Harmony of Dissonance
Defeat Talos -- Harmony of Dissonance
Defeat the Cyclops -- Harmony of Dissonance
Defeat Maxim -- Harmony of Dissonance
Collect all the furnitures -- Harmony of Dissonance
Save Lydie & Maxim, beat the game -- Harmony of Dissonance
Beat the game as Maxim -- Harmony of Dissonance
Collect all the souls -- Aria of Sorrow
Beat the game as Julius -- Aria of Sorrow
Beat the game -- Dracula X / Vampire's Kiss
Save Maria -- Dracula X / Vampire's Kiss
Save Annet -- Dracula X / Vampire's Kiss