Shadow Milotic

Shadow Milotic doesn't really stand above its basic forme to any great degree. It was never good in Raids, so its primarily utility is as a defender... and guess what stat gets lowered when a Pokemon get shadow-boosted?

Milotic won't last quite as long on defense, and the Attack boost doesn't really matter to any great degree. It's still fine, but not really worthy of investment.

Best PvE Offensive Moveset

• Waterfall paired with Surf makes Milotic’s most useful attacking set, with a performance that slightly trails Vaporeon.

• Dragon Tail should be paired with Blizzard if you’re desperate for a Dragon-type counter.

• Hyper Beam and Wrap have no purpose on an offensive MIlotic.  

Best PvE Defensive Moveset

• Dragon Tail edges out Waterfall because it is not resisted by Grass, although Waterfall is better against Electric-types.

• Wrap is generally the charged move of choice, as it has good neutral coverage, decent power, and a low energy cost.
• Surf has stronger damage output thanks to STAB, but it also comes out less frequently.
• Blizzard is risky due to its high energy cost, but if it comes out then it's going to cause a lot of damage.
• Hyper Beam is a bit stronger against neutral targets when compared to Blizzard, but it's also easily dodged.

Dragon Tail is a fairly good move in PvP, with decent energy gains and a narrowly resisted offensive type. Waterfall could be chosen for strong STAB damage, but its slow energy gains makes it harder to use charge moves. 

Surf is a solid Water-type attack, sporting good power, low energy cost, and STAB. It will generally be Milotic's main attack, with the very slow Blizzard or Hyper Beam standing as backups. The former mainly threatens Grass and Dragon, while the latter offers neutral coverage on Water- and Ice-types.