As wedrownik said, just click duplicate to create a copy of the selected animation.
You can mix the two animations at runtime, and see how it will look like in the preview view.
You could also duplicate the attack animation, then select all the frames in the walk animation, copy them, and paste them on the attack animation, this works best if the bones you're pasting can be independent from the already present keys on other bones, e.g. An arm and the cycle of a leg, if you empty the dope sheet for the arm bone and paste the attack animation, you'll obtain a hybrid animation.