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