Here is the full list of all 42 Horizon achievements.
The base game contains 30 achievements, and there is 1 DLC pack containing 12 achievements.
Build 10 ships
Colonize 10 planets
Play for 100 years
Complete the Lezgoon missions
Skip all tutorials
Complete the tutorial without skipping any steps
So, we're not alone then?
Complete the Kor'tahz missions
Complete the Varaian missions
Complete the Barbeck missions
Complete the Barsig missions
Complete the Gargal missions
Complete the Har'kan missions
Complete the Kamzak missions
Complete the Kuntari missions
Complete the Tantik missions
Build 100 ships
Build 1000 ships
Colonize 100 planets
Colonize 1000 planets
Scrap 10 ships
Scrap 100 ships
Scrap 500 ships
Level 1 tech to level 10 in a single game
Level 10 techs to level 10 in a single game
Level 40 techs to level 10 in a single game
Level 80 techs to level 10 in a single game
Play for 1000 years
Play for 10,000 years
Play for 100,000 years
Terraform 10 planets
Terraform 100 planets
Terraform 500 planets
Victory by Conquest
Victory by Conquest at Hard Difficulty
Victory by Conquest at Very Hard Difficulty
Victory with Alliances
Victory with Alliances at Hard Difficulty
Victory with Alliances at Very Hard Difficulty
Victory via Galactic Council
Victory via Galactic Council at Hard Difficulty
Victory via Galactic Council at Very Hard Difficulty