The above guides are good for the respective seals, but I haven't seen one that focuses on the Dredgen seal yet. This one involves quite a bit of Gambit, Destiny 2's new gamemode.
Down below are the main actions you need to perform to obtain this Triumph Seal.
1. Complete the Gambit Collections Badge (only has to be for one class).
This includes most items obtained through the mode, those being:
All Gambit weapons and armour are available as random drops from Gambit bounties.
Bygones - Pulse Rifle - Random drop OR vendor roll available from the Drifter after hitting the rank of Mythic I
Hazard of the Cast - Auto Rifle - Random drop
Pillager - SMG - Random drop
Parcel of Stardust - Shotgun - Random drop
Dreaded Venture - Sniper Rifle - Random drop
Trust - Hand Cannon - Random drop OR the Mysterious Package you get for resetting your Gambit rank once
Distant Relation - Scout Rifle - Random drop
Bad Omens - Rocket Launcher - Random drop OR the Enigmatic Package you get for resetting your Gambit rank twice
Malfeasance - Exotic Hand Cannon - Complete the Exotic Quest obtained through killing the Ascendant Primeval Servitor (the boss that looks like the final Forsaken campaign one). The full quest is explained under triumph 11: Aim to Misbehave.
Ancient Apocalypse Head Armour - Random drop
Ancient Apocalypse Arms Armour - Random drop
Ancient Apocalypse Chest Armour - Random drop
Ancient Apocalypse Leg Armour - Random drop
Ancient Apocalypse Class Item - Random drop OR vendor roll available from the Drifter after hitting the rank of Heroic I
Playin' the Odds Emblem - Speak to the Drifter
Gambit Chrome Shader - Dismantle a weapon with the shader on it, easiest is the Trust from the Mysterious Package
Furtive Ghost Shell - Reset your Gambit rank three times (this can be done over multiple seasons), then buy it from the Drifter
Antediluvian Sparrow - Random drop from the Ascendant Primeval Servitor after obtaining the Malfeasance quest
Drift Apart Ship - Random drop from the Ascendant Primeval Servitor after obtaining both the Malfeasance quest and the Antediluvian sparrow
2. High-Value Hawk Triumph - Kill a High-Value Target of every species.
Whenever the Drifter announces that there's a high-value target on the field, find it and kill it. The triumph requires you to kill one of each species (Fallen, Vex, Hive, Cabal and Scorn).
3. Light Versus Light - Defeat an invader while their Super is active ten times.
Best thing to use is the Sleeper Simulant since it deals a lot of damage to invaders in their super, often outright killing them.
Edit: This triumph has changed to also count kills from invaders on enemies with their Super active.
4. Gambit for All Seasons - Win a Gambit match against every species.
Play Gambit and this will come naturally.
5. Dark Age Arsenal - Win a Gambit match wit a Gambit weapon equipped in every slot.
Self-explanatory. You need the Bad Omens rocket launcher, either the Trust hand cannon or the Distant Relation scout rifle and one of the following: Bygones, Pillager, Hazard of the Cast, Dreaded Venture or Parcel of Stardust.
EDIT: Gambit Prime weapons (Night Watch, Spare Rations, Gnawing Hunger, Last Man Standing, Doomsday) also count.
6. Prestige - Reset your Infamy rank once.
Reach 15000 Infamy and then hold
over the Gambit icon until the bar is full.
7. Army of One - Kill four enemy Guardians in a single invasion three times.
Best would be a weapon with range like a Linear Fusion Rifle or a Sniper Rifle. Thunderlord is also very good for this since it has a lot of ammo per brick. Other strong weapons for this are Truth and Xenophage.
8. Half-Banked - Deposit 38 or more Motes in a single round five times.
Collect motes and bank them in increments of 5 or 10 to avoid losing them to invaders or NPC enemies.
9. Thrillmonger - Defeat forty enemies in a match without dying three times.
Instead of focusing on collecting motes, focus on clearing NPC's and hide from invaders when necessary.
Edit: blocker types have changed with Phalanxes being replaced by Goblins.
10. Protect the Runner - Win a game where someone on your fireteam deposited 75 motes without losing any.
This is a tricky one due to the requirements, but the best thing to do is to play in a full fireteam and have one designated mote collector who will also hide from invaders. He can die when he is holding no motes.
EDIT: Someone in the comments pointed out that 75 motes is enough.
11. Aim to Misbehave - Acquire Malfeasance.
This is quite a long quest which requires you to kill the Ascendant Primeval Servitor once to start.
Step 1: The Seething Heart - Speak to the Drifter.
Step 2: City of Secrets - Kill 25 Taken bosses or minibosses in the Dreaming City. Best option would be to repeatedly do the Corrupted strike.
Step 3: The Corrupted - Complete the 580 power level mission variant of the Corrupted Strike. There is no matchmaking for this and it's quite tough, so make a fireteam before starting this mission.
Step 4: Depleted Weapon Core - Deliver the item obtained in the previous mission to the Drifter.
Step 5: Business as Usual - Bank 400 motes. Every mote you lose subtracts two motes from your total. Win 10 Gambit matches.
Step 6: Lights Out - Kill 25 Guardians and either obtain one Army of One medal or have a team member obtain three Army of One medals.
Step 7: Dark Weapon Core - Speak to the Drifter to obtain Malfeasance.
Let me know if there's things you want added and good luck slaying those Primevals!
Major edit: With Season of Arrivals, the Collections Badge is no longer needed for the triumph seal.