Dredger Style

The unlock criteria for each of these styles is the quest in which you give the item to your butler. This means that you don't have to use each item if you don't want to, but it also means that the [item=184446] you pick up during the initial questline doesn't count toward the achievement.

Sources:

Style

Item

Source

Black Muck Armor Dye

[item=182702]

[npc=171808] at The Night Market (price changes weekly)

Blue Muck Armor Dye

[item=182705]

Enemies or [object=353947] in Dredgewood

Green Muck Armor Dye

[item=182704]

Enemies or [object=353947] in Muck Pool: Banewood

Bubbling Muck Armor Dye

[item=182703]

Enemies or [object=353947] in Blistering Bog

Thin Hair Cut

[item=182970]

[object=351545] in the Ember Ward

Spikey Hair Cut

[item=182972]

Creatures in the Endmire

Full Flowing Hair Cut

[item=182971]

[object=358318] in Redelav Tower

Dredger Lether Coif

[item=182973]

[npc=164966] above Sinfall for 10 [currency=1820] (requires Honored)

Short Sleeved Doublet

[item=182712]

Treasures in Revendreth

Long Sleeved Doublet

[item=182967]

[npc=161310]

Superb list by taaruk!
But for anyone who just opens this page and doesn't want to go any further this might help:

Executioner Adrastia - /way 43.70, 51.21
Fabius's Portrait - The tower is accessed from the mirror inside Thornhill Manor, entrance at /way 59.23, 30.28 - Found on the top floor of the Redelav Tower in the far right corner.
Ta'tru - /way 51.12, 78.75

Vial of Blue Muck Dye - Discarded Vial in Dredgewood /way 74.63, 74.96
Green Muck Dye - Discarded Vial in Muck Pool: Banewood /way 53.18, 72.74
Bubbling Red Muck Dye - Discarded Vial in Blistering Bog /way 35.64, 32.90

Spikey Hair Cut - this personally dropped from Endlurker and on an alt Famu - but its worth noting it'll drop from every mob at /way 27.70, 48.56

In addition to Taaruks excellent post, I'd like to point out that you can further equip your butler with mounts. These can be bought from [npc=164966]:

• 
  
• [item=183842] - ground mount. Requires revered reputation with [faction=2445], costs 55 [currency=1820].
• 
  
• [item=183843] - flying mount. Requires exalted reputation [faction=2445], costs 70 [currency=1820].
• 
  

This works similar to [item=44998] using a pony [item=47541].