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.
You have acquired Kablooey
You have found half of the Lost Souls
You have defeated Mundus' spawn
Completed a mission with a SSS rank
You have acquired Revenant
You have acquired Aquila
You gained a SSS Style Rank during combat
You have acquired the Devil Trigger ability
You helped Phineas by retrieving his eye
You have acquired Eryx
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
Help Vergil open the Vault
Defeat Mundus
Complete the final mission on Human, Devil Hunter or Nephilim difficulty
Complete a level without taking any damage
Complete Furnace of Souls without taking damage from the furnace
Kill 10 enemies by pushing them into the Hurricane ride on Mission 1
Reach the end of the descent on Mission 6 having killed all of the enemies
Navigate the Sky Bridge on Mission 16 without hitting the lasers
Complete a level with 2 minutes or less on the clock
Kill 50 enemies using nothing but firearms
Kill 100 enemies using nothing but Demon weapons
Kill 100 enemies using nothing but Angel weapons
Slay 1,000 Demons
Slay 5,000 Demons
Earn 1,500 Style Bonuses
Spend 10,000 Red Orbs
Spend 50,000 Red Orbs
Upgrade Dante's health to maximum
Upgrade Dante's Devil Trigger to maximum
Purchase all of Dante's combat upgrades
Find all of the Keys
Open all of the Secret Doors
Free all of the Lost Souls
Gain a 100% completion rank on all missions (difficulty doesn't matter)
Complete all missions on the Son of Sparda difficulty
Complete all missions on the Dante Must Die difficulty
Complete all missions on the Heaven or Hell difficulty
Complete all missions on the Hell and Hell difficulty
Complete all missions on the Nephilim difficulty with a SSS rank
Complete 10 Secret Missions
Complete all of the Secret Missions
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)