Here is the full list of all 99 Devil May Cry HD Collection achievements. It takes around 60-80 hours to unlock all of the achievements on Windows.
DMC: Clear a mission without taking damage
DMC: Finish the game without using any Yellow Orbs
DMC: Finish the Game on Hard Mode
DMC: Complete all Secret Missions
DMC: Purchase all of Dante's Skills
DMC: Collect 50,000 Red Orbs
DMC: Complete six Secret Missions
DMC: Achieve an S Rank on any Mission
DMC: Complete a Secret Mission
DMC: Collect 25,000 Red Orbs
DMC: Collect all Guns
DMC: Finish the game on Normal Mode
DMC: Defeat Mundus
DMC: Unlock every enemy file in the status menu
DMC: Defeat Nightmare
DMC: Fight Nightmare a second time and prevail
DMC: Defeat Nelo Angelo
DMC: Survive an encounter with Nightmare
DMC: Perform an S Rank Combo using Ifrit
DMC: Defeat Griffon
DMC: Collect 10,000 Red Orbs
DMC: Fight Griffon a second time and prevail
DMC: Fight Nelo Angelo a second time and prevail
DMC: Unlock 50% of all entries for every enemy file in the status menu
DMC: Survive an encounter with Griffon
DMC: Defeat Phantom
DMC: Survive an encounter with Nelo Angelo
DMC: Survive an encounter with Phantom
DMC: Complete a Blue Orb
DMC: Perform an S Rank Combo using Alastor
DMC2: Finish the game on Normal Mode with any character
DMC2: Finish the game on Hard Mode with any character
DMC2: Finish the game on Must Die Mode with any character
DMC2: Finish the game on any difficulty with Trish
DMC2: Complete a Secret Mission
DMC2: Pass 1000 levels in Bloody Palace Mode
DMC2: Pass 5000 floors in Bloody Palace Mode
DMC2: Pass 9000 floors in Bloody Palace Mode
DMC2: Achieve an S Rank on any Mission with Dante
DMC2: Achieve an S Rank on any Mission with Lucia
DMC2: Max out Health Bar with any character
DMC2: Max out Devil Trigger Gauge with any character
DMC2: Collect 12 Blue Orb fragments (Dante/Lucia)
DMC2: Defeat Tartarussian
DMC2: Defeat Orangguerra
DMC2: Defeat Jokatgulm
DMC2: Defeat Nefasturris
DMC2: Defeat Tateobesu
DMC2: Defeat Noctpteran
DMC2: Defeat Bolverk
DMC2: Defeat Plutonian
DMC2: Defeat Phantom
DMC2: Defeat Trismagia
DMC2: Defeat the final boss with either Dante or Lucia
DMC2: Perform an S Rank Combo using Dante
DMC2: Perform an S Rank Combo using Lucia
DMC2: Reach Level 3 on any Sword with Lucia
DMC2: Reach Level 3 on any Gun with Dante
DMC2: Reach Level 3 on all Swords with Dante
DMC2: Reach Level 3 on all Arsenals with Lucia
DMC2: Collect all Swords with Dante
DMC2: Collect all Arsenals with Lucia
DMC2: Collect all Devil Hearts with Lucia
DMC3: Reach the highest level for any gun with Dante.
DMC3: Max out the Devil Trigger Gauge with Dante.
DMC3: Max out the Health Bar with Dante.
DMC3: Reach the highest level in all Styles with Dante.
DMC3: Clear every mission in Yellow Orb Mode.
DMC3: Defeat Jester in all of his forms.
DMC3: Purchase all Devil Arm skills with Dante.
DMC3: Defeat Arkham.
DMC3: Defeat Doppelganger.
DMC3: Defeat Lady.
DMC3: Fight Vergil a second time and prevail.
DMC3: Defeat Geryon.
DMC3: Defeat Beowulf.
DMC3: Defeat Nevan.
DMC3: Defeat the Heart of Leviathan.
DMC3: Survive an encounter with Vergil.
DMC3: Defeat Agni and Rudra.
DMC3: Defeat Gigapede.
DMC3: Defeat Cerberus.
DMC3: Achieve an S Rank on all missions (any difficulty or character).
DMC3: Achieve an S Rank on any mission with any character.
DMC3: Complete Bloody Palace Mode.
DMC3: Pass 5000 levels in Bloody Palace Mode.
DMC3: Pass 666 levels in Bloody Palace Mode.
DMC3: Kill 100 enemies during the credits.
DMC3: Complete all Secret Missions with any Character.
DMC3: Complete a Secret Mission with any character.
DMC3: Finish the game on any difficulty as Vergil.
DMC3: Finish the game on Heaven or Hell Mode with any character.
DMC3: Finish the game on Dante Must Die Mode with any character.
DMC3: Finish the game on Very Hard Mode with any character.
DMC3: Finish the game on Hard Mode with any character.
DMC3: Finish the game on Normal Mode with any character.
DMC: Max out the Health Bar
DMC: Unlock all the entries for every enemy file in the status menu
DMC: Finish the game on Dante Must Die Mode