the achivements that you can obtain

General: In the general category you have most of your random and miscellaneous achievements. Some are rather easy like obtaining a non-combat pet, falling really far without dying, owning a tabard, the riding LOTRO Gold skills, reaching level 10/20/30/etc, and weapon skills.
PvP: Full of achievements that range from getting a certain number of honorable kills, getting the killing blow on certain classes and battleground specific ones.
Exploration: Exploring zones to 100%.

Here are some achivements that you can obtain. This information is fresh from the latest build of the beta so it is proably going to change. There are some achievements are as follows:
Quests: The quest category you have 1,000 to 1,500 quests as the top ones with daily quests, nesingwary, World of Warcraft Gold rewards from quests, and completing a certain amount of quests in certain zones.

Reputation: Gaining exalted with various reputations give the majority of these.
Feats of Strength: None known by me currently. It looks like it'll be things that you do that are noteworthy but won't give you any points.
That is the achievements you can see them from the beta, they may change a lot now and pay more attention to the change.

Professions: Getting to certain skill levels of professions get the major ones where as there is currently some specific ones to Cooking, Fishing, and First Aid. Fishing up certain items, bandaging at certain times, and a Portal reference with an achievement named "The Cake Is Not A Lie" where the goal is to bake a delicious chocolate cake.
Dungeons & Raids: Basically killing certain bosses on certain difficulties grants you certain achievements. A funny note about the beta is a temporary achievement for soloing Onyxia.
World Events: Doing things during most holidays give you achievement points.