Okay, it can't get Ice Shard, but hope this helps:
Avalugg (M/F) @ Leftovers Trait: Sturdy EVs: 252 Atk, 4 Def, 252 HP Nature - Avalanche - Curse - Earthquake/Stone Edge - Recover/Rapid Spin
Upon farther investigation, I've found Avalugg to be a bit more Viable in competitive play. Its limited STAB movepool prevents it from getting Ice Shard and other great physical Ice moves, but Avalanche still packs a punch as long as he tanks physical hits. With curse it'll just boost his already great Atk and Def stats while getting rid of speed that it already doesn't have, while Earthquake gives it steel, rock and fire type coverage. Though Stone Edge would help against Talonflame, EQ is a better for overall coverage. If you plan to get a wall going then recover is a good asset, but if you need a spinner go with RS.