Pokémon X and Y Walkthrough, Pokémon Move Sets: Avalugg
(Please note that the recommendations below are largely made for in-game play. An Avalugg in a competitive environment will likely make use of different moves to accommodate for smarter, more adaptive opponents. If you have an alternate moveset, share it with the world in the comments.)
Pokémon run the gamut from birds to magnets to living snowflakes, but never before has the series catered to lumbering, living glaciers. Enter Avalugg, a newcomer to the scene with just as much defensive heft as you'd expect looking at its picture. Avalugg isn't quite as well-protected as you might hope, but with some tweaking it can become one dilly of a pokémon.
Avalugg begins life as Bergmite, a shy little creature that remains that shy until it hits level 37. Get up to that level and you've got yourself an Avalugg.
Fighting, Fire, Rock, Steel.
Ice-types get a bit of a raw deal when it comes to weaknesses, so they often need to make up for it stat-wise. To an extent, Avalugg does just that. True, it has absolutely abysmal Special Attack and Special Defense, and it's just about the slowest pokémon on the planet, but it has a healthy amount of HP, its Attack is monstrous, and its Defense is danged near insane. Try to attack an Avalugg with a special attack and you're likely to bring it down; try to attack that same Avalugg with a physical attack and you'd be hard pressed to bring it down in three or four hits, even if you are using a super effective move.
Own Tempo: The pokémon is immune to confusion attacks. This is helpful if you anticipate, say, Stagger, but not enough pokémon are likely to confuse your Avalugg. Own Tempo isn't bad, it's just not the better of the two abilities.
Ice Body: The pokémon recovers a portion of its health if there is currently hail in the battle. Give an Ice Body Avalugg Hail, along with, oh, Leftovers, and you've got a beast that just won't go down.
Sturdy: If the pokémon is at full health when hit by a move strong enough to take it down, Sturdy will ensure that it remains alive with a single HP. Sturdy is terribly annoying when you're on the wrong side of it, and fantastic considering how vulnerable Avalugg is to special attacks. This is a hidden ability.
Avalugg has the raw Attack stat to make it a fantastic tank, and a good enough move pool to cover a few move types outside its native ice. Avalanche is Avalugg's standout move, taking advantage of Avalugg's terrible Speed by allowing the enemy to get in a single hit and doubling Avalanche's attack power. Couple that with Return, Crunch, Earthquake and Stone Edge and you've got one terrifying powerhouse of a pokémon... assuming it can survive the first round.
The alternative here is to make Avalugg into a slightly hardier pokémon with some supportive moves. Hail will keep your Avalugg kicking if you have one with Ice Body, Recover is great for emergencies, and Curse will make Avalugg an even tougher hitter than usual while sacrificing virtually nothing on Speed. (There's nothing to sacrifice, you see.) Rapid Spin is a possibility if you like to get rid of Spikes, though I suggest bolstering Avalugg's offenses instead. Regardless of your moveset, make sure you have Avalanche! There's no pokémon better suited to using Avalanche than its namesake!
One last suggestion: employ a pokémon with either Light Screen, or a move that will boost Special Defense coupled with Baton Pass. Avalugg's Special Defense is truly pathetic, and even with EV training it's not likely to survive more than two hits from special attacks. Bring in a weakness and you can kiss your poor ice-type goodbye.
EV / Super Training
Attack should be your priority with an Avalugg. Get this up to max and Avalugg will rip pokémon apart with Avalanche, whether it's super effective or not effective at all. Defense can use a few points, but not too many - this thing will get plenty of Defense as it is. HP isn't a bad idea to offset damage done by special attacks. Special Attack itself and Speed are negligible concerns, and should largely be avoided.
The big question here is Special Defense. Should you bother? The answer is... it depends. If you plan on selectively deploying your Avalugg and know what's coming, eh, no, don't bother. Stick with training Attack and HP. If you want to prepare for the unknown, on the other hand, pumping a large number of points into your Avalugg isn't a terrible idea. These things can usually wipe out an enemy pokémon in one hit, and in my experience pokémon that make heavy use of their Special Attack stat are a little fragile against physical thwompings. If you DO decide to raise an Avalugg with a decent Special Defense, get one with an appopriate Nature that will help you along. Sassy or Careful are good choices.
Catching an Avalugg
As mentioned above, Avalugg evolves from Bergmite at level 37. This necessitates catching yourself a Bergmite. Fortunately, there's one very obvious place to do that: the Frost Cavern near Dendemille City. They're a little uncommon, but it shouldn't take more than ten minutes of searching to track an appropriate Bergmite down.