Walking animation and attack animation at same time?

Is it possible to have the sprite (moving with the 8-direction movement) perform an attack animation while the walk animation is also going on? Basically I want my sprite to look like he's walking and punching.

Sure.

You could seperate the leg animation from the upper body.

Or seperate the arms as an individual animation.

Or create an additional full body animation that combines both walking and punching. Then switch to the combined animation whenever it's needed.