I have taken a taxi there before, of course it can be done. However, Rio can be a dangerous city. Dress down and leave the Rolex at home. Don't carry an expensive camera AND a big bag that looks like it is full of expensive things.
Yes, you can do Ipanema on your own. Take into consideration what Paul said and only take the essentials and go during mid-day. Stay to the beach area and you'll be fine but just use common sense like in any large area.
A cab will run you about $25 from the cruise ship port that Azamara uses, or at least did on our December cruise.
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"There is a great difference between being well traveled and just having been to many places." ~Me