When playing songs that require fast picking, like most Amon Amarth tunes, I tend to move my arm more then my wrist to do the picking and I grow tired very quickly.

Any advice on how to get my wrist to do the picking?
Guitar/bass/mandolin stuff:
PRS SE Custom 24
PRS SE Paul Allender
Martin DCX1E
Squire Start
Memphis Bass
Johnson Savannah mando

Digitech RP1000
Line 6 Spider Valve 212
Toneport Studio KB37

check out my last.fm!
Don't play fast. Play very slow and make sure that you do not move your arm. Keep still and move your wrist only. Make sure that there is no tension and that you feel comfortable doing this. Really the key is, don't even try to play music, just hit a few notes slowly until you can get it down. Increase tempo as you get more comfortable but I can't stress enough that playing it comfortably slow is way better than trying to rush into a song doing something you're not familiar with.
Go slow. That's the only way. Try to play at a lower tempo and ensure that your wrist moves in a limited manner. This exercise may help you. This is all on the high e string.

8 5 7 8 7 5.

It's in the key of C major. While practising this, just ensure that the movement of both your arms and wrists are limited. Even when you playing, ensure that the fretting hand doesn't move away from the guitar much.

BTW I believe it is a Paul Gilbert exercise.