Here is the full list of all 26 Trident's Wake achievements.
Cause a Zodiac to detonate by shooting at it.
Complete a mission with High Enemy Pressence without any Sentinel loss.
Complete a 4-player mission with everyone alive at extraction.
Complete a mission with at least one more player in your squad.
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.
Customize a Sentinel's chassis colors.
Cause a Zodiac to detonate, and have its explosion take out another Zodiac.
Kill a Specter while it's invisible.
Complete a mission with over 80% accuracy.
Hit 4 or more enemies with a single shot from the Railgun.
Have one enemy receive the full impact of one Shotgun blast.
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.
Kill one enemy of each type.