First off, you can only obtain Azumarill by evolving an Azurill found in Brawler's Cave (Which is a location included in the Isle of Armor) or by trading for an Azurill, Marill, or Azumarill.
Azumarill is a great physical attacker if it has the ability Huge Power, which doubles it's Attack stat. Sap Sipper (HA) and Thick Fat are both decent abilities, but Huge Power is way better. I'd recommend only using Azumarill if you can find one with Huge Power.
Azumarill's stats aren't great, but that doesn't matter too much for in-game playthroughs. The only stat it really excels in is HP, at 100 base.
Azumarill @ Mystic Water / Pixie Plate
Ability: Huge Power
- Aqua Tail (Learned at lv. 21)
- Play Rough (Learned at lv. 29)
- Double-Edge (Learned at lv. 45)
- Ice Punch / Dig (TM bought at Wyndon Pokecenter [Ice Punch] / TM found on Route 6 [Dig])
Azumarill gets fantastic moves by level-up, so you won't be using many TM/TRs on it.
With this moveset, Azumarill can do great against foes like Raihan (Dragon), Piers (Dark), Marnie (Dark), Kabu (Fire), Bea (Fighting), Gordie (Rock), Leon's Dragapult / Haxorus / Charizard (As well as a few others depending on which starter you pick), and Hop's Silicobra / Heatmor / Rillaboom*. Water and Fairy is a great offensive type combo for this game.
Overall, I'd say Azumarill is a great pick for your team if you can get a Huge Power one.
(*If you pick Scorbunny.)