I'm sure it's possible, but I can only speculate what you are doing wrong.
Your current two animations (attack and shield) probably "overwrite" each other, because they include movements of all body parts. If you make attack animation to only move one hand with a weapon, and shield animation to only move another hand with the shield, then you may be able to play both simultaneously. You'll probably need a third animation for the remaining body parts.
But again, this is only a guess, I may be completely wrong