Full list of all 58 DmC: Devil May Cry achievements worth 1,250 gamerscore. It takes around 40-50 hours to unlock all of the achievements in the base game.
The base game contains 48 achievements worth 1,000 Gamerscore, and there is 1 DLC pack containing 10 achievements worth 250 Gamerscore.
Completed all missions on Heaven Or Hell difficulty
Completed all missions on Hell and Hell difficulty
Completed all missions on the Nephilim difficultly with a SSS rank
You have slayed 5,000 Demons
You completed Furnace of Souls without taking damage from the furnace
Completed all missions on the Dante Must Die difficulty
Completed all missions on the Son of Sparda difficulty
You have Spent 50,000 Red Orbs
You have purchased all of Dante's combat upgrades
You have upgraded Dante's health to maximum
You have completed all of the Secret Missions
You have upgraded Dante's Devil Trigger to maximum
You have completed 10 of the Secret Missions
You earned 1,500 Style Bonuses
You have been awarded a 100% completion rank on all missions
You have opened all 21 Secret Doors
You completed a level without taking any damage
You have found all 21 Keys
You have found all of the Lost Souls
You have slayed 1,000 Demons
You have spent 10,000 Red Orbs
You killed 50 enemies using nothing but firearms
You defeated Vergil on any difficulty
You have defeated Mundus
You helped Vergil open the Vault
You have acquired Kablooey
You navigated the Sky Bridge without hitting the lasers
You completed a level in 2 minutes or less
You have defeated Mundus' spawn
You killed 100 enemies using nothing but Angel weapons
You have acquired Revenant
You have found half of the Lost Souls
You Killed 10 enemies by pushing them into the Hurricane ride
You have acquired Aquila
You have acquired the Devil Trigger ability
You helped Phineas by retrieving his eye
Completed a mission with a SSS rank
You have acquired Eryx
You gained a SSS Style Rank during combat
You reached the end of the descent on Mission 6 having killed all of the enemies
You killed 100 enemies using nothing but Demon weapons
You have defeated the Tyrant
You have acquired the Angel Boost ability
You have slayed 100 Demons
You have acquired Osiris
You purchased your first upgrade
You have acquired Arbiter
You have defeated the Hunter
Defeat a Wisp
Defeat an Imprisoner
Complete Vergil's downfall
Acquire all of Vergil's health, Devil trigger and combat upgrades
Complete all missions in Vergil's downfall on the Nephilim difficulty with a SSS rank
Complete Vergil's downfall on Son of Sparda difficulty
Complete Vergil's downfall on Vergil Must Die difficulty
Complete Vergil's downfall on Heaven or Hell difficulty
Complete Vergil's downfall on Hell and Hell difficulty
Gain a 100% completion rank on all missions in Vergil's downfall (difficulty doesn't matter)