Here is the full list of all 45 Saints Row: Gat out of Hell achievements. It takes around 20-25 hours to unlock all of the achievements on Windows.
Kill 25 Arch Dukes
Have minions kill 100 Demons with the Summon Supernatural Power
Kill 25 Demons with each of the Seven Deadly Weapons
Get 250 kills with the Essence of Wrath
Get 100 kills with the God's Hammer
Kill 150 Demons with the Stomp Supernatural Power
Fly for 250,000 meters
Beat the game
Conquer all of New Hades with 100% City Take Over
Purchase 113 Supernatural Power Upgrades
Find 100% of all Soul Clusters
Complete all open world gameplay in two districts of the city of New Hades
Get 250 kills with the Essence of Sloth
Take down an Extraction Facility while on a motorcycle
Find 75 Barnstorming Diversion locations
Car surf on a Comet while it explodes
Find 64 Tomes
Get a Comet into the Ultor lobby
Kill 50 of your own summoned Imps
Choose a new element for all of your Supernatural Powers
Stand on the tallest mast of the 'Queen Anne's Revenge'
Play for at least 2 hours as Gat and 2 hours as Kinzie
Fly from the roof of Snowball's Chance to Sinterpol HQ's roof, without landing
Smack into the ceiling 10 times while wall running
Stonify and Shatter Kill 100 Demons with the Stone Blast Supernatural Power
Fly for 500 meters while on fire
Fly continuously for 60 seconds
Knock a vehicle into the lava
Upgrade one weapon to the max
Kill an Arch Duke with a melee attack
Die in the lava
Stay in contact with the lava for 10 seconds without dying
Be airborne during Supernatural Jumps or Flight for a combined 10 minutes of gameplay
Have five Imps attached to you at one time
Find 100 Soul Clusters
Buy your first Upgrade from the Upgrade Store
Collect at least five Soul Clusters without touching the ground
Get your first Supernatural Powers
Kill 100 Demons using the Coldfire Aura Supernatural Power
Kill 1000 Demons with any combination of Supernatural Powers
Complete ALL of the Challenges
Play Saints Row: Gat out of Hell Co-op for 3 hours
Shoot down a Spire missile with a blast while hovering
In Torment Fraud, hit 5 vehicles in a row without touching the ground
Spend over 20 hours in Hell