Speak to the client on the phone, listen and explain back to them what you have understood they are complaining about. A lot of the trouble with complaints is that clients don't feel you understand them.
Don't be afraid to apologise. You don't have to agree you've made a mistake, indeed you cannot, as doing so may invalidate our insurance, but you can apologise for the way they feel or that they have had to complain, for example.
Often there is no need to bat back all points. Once you've listened to them you can propose a way forward, that is usually enough.
It's often a good tactic to rehearse where you are in the matter and why. Don't shy away from pointing out all the good things that you've done, i.e. progress made, valuable work done, goals achieved.
If you can resolve it, then make sure it's 100% closed off. Thank the client on the call and follow up in writing, noting it's all been addressed to his satisfaction. Then make sure you are seen to be doing what you'd agreed to do in short order.