I currently have a nanny that we are trying to let go as well and am struggling with the same thing. Fortunately, my husband has no trouble being confrontational and so he is going to do the letting go (as soon as we find a replacement). Our nanny isn't as bad as you've described yours, but we are still dealing with laziness, poor judgement, inability to use critical thinking skills,runs personal errands without permission, talks on her phone ALL freakin' day, and we suspect her of stealing.. ugh!
If it's too hard to tell her why you're letting her go, either tell her you've decided you no longer need a nanny and therefore there's just not a position for her at this time, or tell her she's just not a good fit for your family and leave out the details... or if you're married, have your husband do it.
Good luck!