Here is the full list of all 89 Hero Siege achievements.
Kill Mevius on nightmare difficulty
Kill Satan on nightmare difficulty
Kill Karp King on nightmare difficulty
Kill Damien on nightmare difficulty
Clear a Chaos Tower
Kill Anubis on nightmare difficulty
Kill Grim Reaper on nightmare difficulty
Kill Gurag on nightmare difficulty
Kill Mevius on normal difficulty
Kill Satan on normal difficulty
Kill Karp King on normal difficulty
Kill Damien on normal difficulty
Kill Anubis on normal difficulty
Kill Grim Reaper on normal difficulty
Kill Gurag on normal difficulty
Complete normal difficulty on Softcore
Complete nightmare difficulty on Softcore
Kill Mevius on hell difficulty
Reach Level 100 with a Hero
Collect 100,000 Gold
Reach Level 90 with a Hero
Reach Level 80 with a Hero
Reach Level 70 with a Hero
Kill 5000 Ancient Monsters
Slay 6400 Monsters
Destroy Satan's both hands in less than 30 seconds!
Reach Level 60 with a Hero
Reach Level 50 with a Hero
Obtain a Satanic Item
Join Sarcaster's Coffee Club
Reach Level 10 with a Hero
Reach Level 40 with a Hero
Reach Level 30 with a Hero
Reach Level 20 with a Hero
Slay 1600 Monsters
Slay 400 Monsters
Slay 100 Monsters
Kill Grim Reaper on hell difficulty
Kill Gurag on hell difficulty
Slay 25400 Monsters
Slay 50000 Monsters
Kill Anubis on hell difficulty
Kill Karp King on hell difficulty
Complete normal difficulty on Hardcore
Kill Damien on hell difficulty
Complete Hell Difficulty on Hardcore
Collect 1,000,000 Gold
Kill Satan on hell difficulty
Obtain level 100 with Viking, Pyromancer, Marksman, Pirate, Nomad, Redneck and Necromancer
Complete nightmare difficulty on Hardcore
Slay Damien in Fallen Inoya
Complete hell difficulty on Softcore
Complete the Halloween quest chain
Complete the Christmas quest chain
Slay King Rakhul in the Chaos Tower
Enter the Angelic Realm
Slay Sung Lee in the Eternal Battle Fields
Obtain 50 Satanic Items
Obtain 200 Satanic Items
Obtain 5 Angelic Items
Obtain 10 Angelic Items
Kill 12500 Ancient Monsters
Kill 20000 Ancient Monsters
Kill Corrupted Odin on nightmare difficulty
Kill Corrupted Odin on normal difficulty
Slay Sung Lee in the Eternal Battle Fields on Hell 5 difficulty
Slay Shadow Reaper in the Shadow Realm on Hell 5 difficulty
Slay Damien in Fallen Inoya on Hell 5 difficulty
Slay King Rakhul in the Chaos Tower on Hell 5 difficulty
Complete hell 5 difficulty on Softcore
Complete hell 5 difficulty on Hardcore
Complete normal difficulty on Odyssey Softcore
Complete nightmare difficulty on Odyssey Softcore
Complete hell difficulty on Odyssey Softcore
Complete hell 5 difficulty on Odyssey Softcore
Complete normal difficulty on Odyssey Hardcore
Complete nightmare difficulty on Odyssey Hardcore
Complete hell difficulty on Odyssey Hardcore
Complete hell 5 difficulty on Odyssey Hardcore
Defeat Gabriel in the Circle of Hatred
Defeat Gabriel in the Circle of Hatred on Hell 5 difficulty