Shadow Alolan Dugtrio

Let's be honest; the only reason to use Shadow Alolan Dugtrio is if you're doing a photoshoot for a shampoo brand. 

Best PvE Offensive Moveset

• If you want to utilize Shadow Alolan Dugtrio for more than just its luxurious, flowing hair, then go with Mud Slap and Earthquake for a Ground moveset, or Metal Claw and Iron Head for a Steel moveset.
• Mud Bomb is underwhelming, as is Return.

Best PvE Defensive Moveset

• Mud Slap is the best Fast Move option on defense, while Mud Bomb is the best Charged Move option. Using the same type for Fast/Charged moves allows other Pokemon to come in virtually uncontested, so it's generally best to run Mud Slap and Iron Head or Metal Claw and Mud Bomb together, but Shadow Alolan Dugtrio is frail enough that it's likely to drop really quickly regardless.
• Earthquake and Return aren't worth considering on defense.