Here is the full list of all 30 Light of Altair achievements.
Found a new colony
Upgrade a colony to Tier 1
Upgrade a colony to Tier 2
Upgrade a colony to Tier 3
Raise fleet level to Experienced
Raise fleet level to Hardened
Build an Aeroponics Dome
Build an Atmospheric Converter
Build a Goods Factory
Build a Hyperspace Gate Stabiliser
Build a Government Building
Build a Nuclear Reactor
Upgrade a colony to a City
Upgrade a colony to a MegaCity
Raise fleet level to Veterans
Raise fleet level to Dangerous
Raise fleet level to Deadly
Raise fleet level to Elite
Win all missions on Normal difficulty
Win all missions on Hard difficulty
10% of objectives complete
20% of objectives complete
30% of objectives complete
40% of objectives complete
50% of objectives complete
60% of objectives complete
70% of objectives complete
80% of objectives complete
90% of objectives complete
100% of objectives complete