Here is the full list of all 26 Trident's Wake achievements.
Customize a Sentinel's chassis colors.
Kill a Specter while it's invisible.
Hit 4 or more enemies with a single shot from the Railgun.
Kill one enemy of each type.
Complete a mission with at least one more player in your squad.
Cause a Zodiac to detonate by shooting at it.
Cause a Zodiac to detonate, and have its explosion take out another Zodiac.
Have one enemy receive the full impact of one Shotgun blast.
Complete a mission with High Enemy Pressence without any Sentinel loss.
Complete a 4-player mission with everyone alive at extraction.
Complete any mission with a 4-player squad.
Complete a mission with "Tougher Enemies" mission modifier enabled, while playing solo.
Complete a mission with "Tougher Enemies" mission modiier enabled, with just one other player.
Complete a mission in which there are three different Sentinels in your squad.
Complete at least one mission with each Sentinel.
Secure a foothold on the Trident (Complete the introduction mission).
Be reconstructed at least three times during one mission.
Reclaim your first sector on the Trident.
You have reclaimed all compromised sectors of the Trident.
Reach Echo Rank 10.
Reach Echo Rank 20.
Reach Echo Rank 30.
Complete a mission with over 80% accuracy.
Hold a Plasma Rifle charge for over 10 seconds, then release it and hit an enemy with the supercharged blast.
Fully upgrade one weapon.
Complete a mission in every sector.