For Adobe Reader 9.5.5 (running natively without Wine)
Don't add the Ubuntu 12.04 Partner repository, you're not really supposed to add repositories from previous Ubuntu versions! Get the Deb from here (source - it's also linked in the question), no it won't be automatically updated but since it's no longer supported (and Ubuntu can't patch security vulnerabilities for it in Ubuntu 12.04 anyway because it's proprietary) that doesn't matter. There's less of a chance you'll ruin your system if you get it this way.
If you can't find/run Adobe Reader, you will need to run sudo apt -f install to resolve dependencies. If it still doesn't work, try sudo apt install libxml2:i386.
This is, of course, a very outdated version of Adobe Reader, but this is not Ubuntu's fault, Adobe haven't updated the Linux client of Adobe Reader. You can, however, get a newer version using the process below (this installs a Windows version of Adobe Reader on Ubuntu).
For Adobe Reader DC 1501020056 (running with Wine 1.9)
- Install PlayOnLinux
- Load PlayOnLinux
- Click 'Install' (in the toolbar)
- Type 'Adobe Acrobat Reader DC' in the search bar
- Click 'Adobe Acrobat Reader DC'
- Click 'Install' (bottom-right)
- Follow the install screens
- Once installed, click 'Adobe Acrobat Reader DC'
- Click 'Run' (in the toolbar)
You'll need to open PlayOnLinux to run Adobe Reader DC each time (note that you can have this installed alongside Adobe Reader 9.5.5). You can drag the desktop file into the Launcher to get a button there, you can also add an icon for it in the Ubuntu Dash using Alacarte ('Main Menu'). I might add instructions for that later. Unfortunately not even this version is completely up to date (there's probably unpatched security vulnerabilities in that version also and Wine is also out-of-date here, though that doesn't matter as much). To install the latest version of Reader, DC or non-DC, you'll need to do so manually using PlayOnLinux. I might write instructions for this or write a POL script to do this at a later date.