Comprehensive information about Beta Achievements & Statistics can be found below. Its a lot of information--take your time!
Feat of Strength
World Events
Lunar Festival
Love is in the Air
Children's Week
Noble Garden
Midsummer
Brewfest
Hallow's End
Darkmoon Faire
Winterveil
General
Quests
Dungeons & Raids
Classic
The Burning Crusade
Wrath of the Lich King
Exploration
PvP
Arena
Alterac Valley
Eye of the Storm
Warsong Gulch
Dungeons & Raids
Classic
The Burning Crusade
Wrath of the Lich King
Professions
Cooking
Fishing
First Aid
Reputation
Statistics
A lot of different statistics, everything from how many deaths to your current alchemy level and much more.
Skills
Alchemy
Enchanting
Travel
Social
PvP (Statistics)
Reputation (Statistics)
Quests (Statistics)
Character
Wealth
Consumables
Gear
Attributes
Damage
Healing
Kills
Creatures
Honorable Kills
Killing Blows
Deaths
Arenas
Battlegrounds
Dungeons
World
Resurrection
Comments
Most things you'll have to do again, obviously the leveling achievements, and the discovery achievements won't be repeatable and you'll be awarded them right away.
Feats of Strength however are awarded instantly if they've been completed