The criterion for getting achievements are sometimes problematic.

There are several achievements where the trigger criteria is picking up an item. These can be earned, or not earned, in unusual ways.
For example, I just achieved Cow Tipper while fishing in the latest snapshot (I caught leather.)

Additionally, the achievements requiring the crafting of wooden tools are problematic.
Crafting a stone hoe or stone sword or stone pick does not unlock Time to Farm! and Time to Strike! and Time to Mine! respectively.
If the starting chest contains a wooden pick, then the player will never construct wooden tools due to the abundance of stone, and then later achievements will be locked even though they have progressed to that "level" of gameplay.
Constructing a stone item should give the respective achievement. Also, constructing a stone pick should give both Time to Mine! and Getting an Upgrade.

The Overkill achievement description says it requires eight hearts of damage, but the achievement actually requires nine hearts of damage.

Repopulation, as its description suggests, only works with cows and not any of the other breedable animals.

For On a Rail, the distance requirement in the description implies travel along 1000 rail blocks. In actuality, the requirement is to travel as the crow flies one kilometer. (I understand why the requirement is like that, to prevent loops etc, but the description is not clear, and this caused me great frustration when I first tried to unlock it.)

Also, there should be a few more achievements:
-Collect a record
-Tame and saddle a horse
-Build a Nether Reactor (Also, this should be added to the PC version)
-Sail a kilometer as the crow flies (Like the On A Rail achievement)
-Change your spawn point via a bed