Anyway, you should realy pay attention to the muting .
For strings above the one your playing (lower strings I mean) , use your picking hand's palm or your fretting hand's thumb.
For strigns below the one your playing (higher strings) , lay down your fretting hand's fingers on them slightly ... or use the right hand's free fingers (if you hold the pick between index and thumb, you'll have 3 fingers free for muting purposes).
If you already know about muting, you should be carefull to tap very precise, your tapping finger (or pick) should be very accurate and have a strong attack.
Also lower string ation will help with tapping , and if you have a comressor put it on.
Good Luck !