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.
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