To fix that mess, you need to remove the bad parts and put in new sheetrock

Not really difficult, but not a first time DIY job without some help from an experienced person.

http://www.drywallschool.com/bigpatch2.htm

Here's a link to give you an idea of what the patching entails

Thanks for the input. Is that something that a professional could fix in one day, or would it take longer with having to wait for drying?

"Is that something that a professional could fix in one day, or would it take longer with having to wait for drying?"

One day if they know how to use quick setting compounds like EasySand20.

It sets in about 20 minutes (it hardens by chemical reaction, not drying out) and a new coat can be applied as soon as the previous coat has set firmly.
I usually take a left over blob and put it aside, then check it for setting.
When the test blob is hard, you can double check the wall and start mixing another batch for the next coat.

If te first few coats are mixed with minimum water shrinkage is not even an issue.

Are you installing the drywall to make the room soundproof? If you're planning to do this on your own, you need to downloas specific guidelines. this is a taxing job so you will probably need an extra hand to complete this job. If you are used into doing home repairs and improvement, this should be an easy job for you, but if you're a newbie, you might want to consider consulting an expert first.

Speaking as an amateur, an amateur could do this. I have done this work, but was helped greatly by having watched a painter do some drywall repair for me.

There are some tools you need to do this. If you have to buy them for a one-time job, it cuts into the savings of hiring someone.

This is a project that I would end up working on over a series of days with multiple trips to Home Depot (as are all my projects). A drywall guy will do it in one day.

Anyone could do the job, but it might not look too good when completed. A pro will make it disappear.