Here is the full list of all 50 Eliosi's Hunt achievements.
Become a bounty hunter
Finish LAB-yrinth
Collect your first Communicator
Unlock the second tier of Upgrades
Finish Gul-karam Desert
Kill three enemies with a single grenade
Shoot twice within 0.075 seconds
Finish The Entity
Kill the Entity
Finish Sieverr's Factory
Destroy a checkpoint
Make your first Upgrade
Finish Lady Swamp
Collect your first drone part
Didn't these devs put any dialog in?
Complete the game without upgrades
Play as the Prototype Guy
Defeat Eizlazir before he launches a single strike
Avoid being captured by the Ordunalos for 40 seconds
Have a bird killed by a Smashing Root
Complete a level having destroyed all its checkpoints (except Lady Swamp and Sieverr's Factory)
Finish a level without dying (except Lady Swamp and Sieverr's Factory)
Have a Vrakio Mercenary killed by an environmental laser
Toast 8 birds in 4 seconds
Kill the Lady Swamp using only the flamethrower
Kill a Well Mutated Ordunalo with 4 different guns
Kill 5 Vrakio Mercenaries with a single shot
Have 8 Beast Guards killed with environmental hazards
Kill a Badly Mutated Ordunalo using only reflected shots
Throw a Hyena to its death
Complete 105% of the game
Dodge 6 kicks from a single Badly Mutated Ordunalo
Collect all of the drone parts in Lady Swamp
Collect all of the drone parts in Sieverr's Factory
Collect all of the drone parts in The Entity
Collect all of the drone parts in Gul-karam Desert
Collect all of the drone parts in LAB-yrinth
Unlock the third tier of Upgrades
Make all the Upgrades
Complete the time goal in Lady Swamp
Complete the time goal in Sieverr's Factory
Complete the time goal in The Entity
Complete the time goal in Gul-karam Desert
Complete the time goal in LAB-yrinth
Collect the bonus item in Lady Swamp
Collect the bonus item in Sieverr's Factory
Collect the bonus item in The Entity
Collect the bonus item in Gul-karam Desert
Collect the bonus item in LAB-yrinth
Complete 100% of the game