Full list of all 42 Star Trek Online achievements worth 1,090 gamerscore. It takes around 200-300 hours to unlock all of the achievements in the base game.
The base game contains 36 achievements worth 1,000 Gamerscore, and there is 1 DLC pack containing 6 achievements worth 90 Gamerscore.
Discovered all the Solanae Dyson Sphere lore
Completed The Iconian War story arc
Discovered all the New Romulus lore
Spent 30 points in any Captain Specialization
Discovered all the Path to 2409 lore
Reached Level 60 with one character
Completed The Delta Quadrant story arc
Completed the Vengeance story arc
Completed the Solanae Dyson Sphere story arc
Completed the In Shadows story arc
Completed the New Romulus story arc
Explored New Romulus
Completed the Allies story arc
Completed the Borg Advance story arc
Got Assimilated by the Borg
Completed the From the Ashes story arc
Reached Level 50 with one character
Completed the Breen Invasion story arc
Completed the Cardassian Struggle story arc
Reached Level 40 with one character
Completed the Romulan Mystery story arc
Reached Level 30 with one character
Completed the Wasteland story arc
Completed the Vigilance story arc
Completed the Fek'Ihri Return story arc
Completed the Warzone story arc
Completed the Empire story arc
Completed the Klingon War story arc
Explored Nimbus
Reached Level 20 with one character
Explored the Risa summer resort
Completed the Spectres story arc
Visited all the Vistas on Risa
Reached Level 10 with one character
Read all of the plaques on Starfleet Academy
Completed a Tutorial
Achieved Level 4 in any Duty Officer commendation track
Achieved Level 15 in one Research and Development school
Achieved Level 10 in one Admiralty campaign
Completed the Future Proof story arc
Completed the Yesterday's War story arc
Completed the Agents of Yesterday story arc