I would like to get this version of Xamarin installed on my machine.
Unfortunately after downloading the Xamarin Updater (nothing appears in updates in the Extensions and Updates window for Xamarin) and uninstalling and reinstalling Xamarin in Visual Studio I still have version 10.10.
There is a bug fix in 10.12 release that I desperately need for my project.
How do I update from 10.10 to 10.12 in Visual Studio 2017?
You can use Xamarin Updater to update to Beta release of Xamarin. In order to do that, you will need to update your Visual Studio to 15.3 preview version first. Then you can follow the steps in this blog to install the Xamarin Updater in Visual Studio 2017. After that, you will have the same updater like you previously have in Visual Studio 2015.
Looking at the documentation from Xamarin found HERE.
To try out pre-release features, you should download the Visual Studio
2017 Preview installer, which will offer the option to install Preview
versions of Visual Studio side-by-side (SxS) with the stable (Release)
version. More information is available in the Visual Studio 2017
Preview FAQ.
So from the looks of it they've switched to 'stable' and 'preview' streams in 2017, and that relates specifically to the VS instance you run. Hit up the link and follow the instructions and you should be golden.
EDIT: Keeping this here just incase (VS 2015 edition)
In visual studio you simply go to tools > options > then you will see a 'xamarin' tab on the left of the options pane.
under each platform (android, and iOS) theres a drop down to switch between 'stable' and 'beta' channels, once you've switched you can force it to check for updates and if there is one available it will prompt you to download and install it.
Hope this helps.