If you could post your sprite I could be more help, but I'll try.
Links awakening Link has a super basic 3 frame attack animation.
http://imgur.com/a/VcP1AThere's the anticipation. There's the action, then there's the end of the action. There's no real followthrough and there's a lot of travel time on the action. These are both bad for conveying snappy action. What you want to do is basically imply the action with a smear. Show the anticipation to teh action, show the charecter at the end of the action, but never show that middle bit. That's what makes something seem slow.
I did a quick mock up fo what I mean.
http://imgur.com/CY6vtTAYou could make it look better with better posing or more frames in the anticipation/recovery, but the key is to make sure you avoid that frame of the weapon traveling. That is what's poison to making something snappy.