Avalugg has higher than average Attack and has a really high defense. However its Speed and Special Attack is really low, but it also have something to overcome its weakness. Unfortunately, even if it can kill Special Attacker with Mirror Coat, it will usually kill only 1 Pokemon because it is too slow to outspeed almost anything and can't use a Priority move
-Has really high Defense and also above averages Attack
-Has access to both Sturdy and Mirror Coat making it able to kill Special Attacker easily
-Has access to Rapid Spin, although it is not the best rapid spinner
-Can use Recover which makes it be able to use Sturdy again
-Being Slow makes it take advantage of Avalanche
- Even being slow gives it advantages, it gets outspeed by most slow Pokemon too
- Even if it can be a Rapid Spinner, Stealth Rock deals 25% of its health to it, also Stealth Rock can make Sturdy useless unless it uses Recover
- Special Attacker can kill it easily if it get hits by Stealth Rock.
Own Tempo: Can rarely be useful, but it still can stop it from being confuse which might come in handy sometime, although Sturdy is a lot better
Ice Body: This ability can only be use in Hail, it could be useful, but it will not have Sturdy to deal with Special Attacker
Strudy: Probably the best Ability for Avalugg, it makes it able to survive Special Attack and hit it back with Mirror Coat or other move like Avalanche
Mirror Coat Avalugg
Item: Leftover/ Lum Berry
Nature: Impish/ Adamant/ Brave/ Relaxed
EVs: 252 HP/ 252 Attack/ 4 Def
Avalanche is Avalugg's best STAB move while Earthquake covers a lot of type Avalanche can't. Mirror Coat can help it to kill Special Attacker and Recover can help it to use Sturdy again after getting attack by Physical move or Entry Hazards. Leftover can help it to get to full health easier after Recover while Lum Berry prevents it from Burn and Poison. I wouldn't put EVs and Natures to Speed because it is too low anyway.
Rapid Spinner Avalugg
Item: Leftover/ Weakness Policy/ Lum Berry
Nature: Adamant/ Impish/ Brave/ Relaxed
EVs: 252 Attack/ 252 HP/ 4 Def
Mirror Coat/ Earthquake
This is the Rapid Spin moveset of Avalugg, even if it isn't the best spinner, it can still work. Avalanche again is the best STAB for Avalugg while Rapid Spin gets rid of Entry Hazards. Mirror Coat can be use again, although you can also use Earthquake instead and use Weakness Policy to OHKO Special Attacker too (or even Physical Attacker). Recover will heal you and lets you use Sturdy again.
Rest: Can work alongside with Chesto Berry, although Recover is a more reliable option
Rock Slide and Stone Edge: Can be use to cover other Ice Type Pokemon, but Earthquake covers Steel which is important
Assult Vest: Can also be use if you put 252 EV on Special Defense and has a Sassy nature, although it will be unable to use Recover or Curse.
Rocky Helmet: Can annoy Physical Attacker sometime
Mega Ampharos is a big counter to Avalugg, since it outspeeds it even if it is slow and can OHKO it with Focus Blast which also breaks through Sturdy thanks to Mold Breaker (it is the only Special Attacker with Mold Breaker though). Anything that has really high attack and can hit it Super Effectively can even OHKO it. Entry Hazards can cut Avalugg's HP up to 50%, forcing it to use Recover or otherwise it cannot use Sturdy. Burn and Poison cripples it as well because those 2 status Condition will make Sturdy useless.
Overall Avalugg can be good, but it would usually knock out 1 or 2 Pokemon at most because it is slow and it lacks priority move.