Let's see below what to check and what steps to use, to successfully upgrade your Configuration Manager 2012 SP1 environment to R2 level:

First you need to check the Upgrade Sequence for the System Center 2012 R2 Suite’s products: http://technet.microsoft.com/en-us/library/dn521010.aspx (In case you have any other SC Products in place, on your environment….)
Then Ensure all sites in the hierarchy run System Center 2012 Configuration Manager with SP1.
(You cannot upgrade a site to System Center 2012 R2 Configuration Manager until all sites in the hierarchy run System Center 2012 Configuration Manager with SP1.The version of cumulative updates for Configuration Manager that are installed at sites is not evaluated and you can upgrade a System Center 2012 Configuration Manager SP1 site
regardless of the cumulative update version that is installed, or even when no cumulative update is installed. ) / From <http://technet.microsoft.com/en-us/library/jj822981.aspx
You may also check, that the deployment of the  updated CM12 SP1 clients is finished and all the client computers, have the correct client version.

Then check in the Monitoring node of the CM12 console for any red  icons (non-OK status), the following:
- Site status
- Component status
- Database replication status

Check also for any issues on:
- Event Viewer.
- SMS logs.

- Select a specific site system server > click Show Messages (status messages) and check for any issues.
- You could even run any Reports related to health on the specific site.
- Another good idea is to stop your Antivirus scanning during the whole process.

Make sure you have a working backup through the CM12 maintenance task preferably (or some other method).
More information you may find here: http://technet.microsoft.com/en-us/library/gg712697.aspx

You can automate backup for Configuration Manager sites by scheduling the predefined Backup Site Server maintenance task. You can back up a central administration site and primary site, but there is no backup support for secondary sites or site system servers. When the Configuration Manager backup
service runs, it follows the instructions defined in the backup control file (<ConfigMgrInstallationFolder>\Inboxes\Smsbkup.box\Smsbkup.ctl). You can modify the backup control file to change the behavior of the backup service. Site backup status information is written to the Smsbkup.log file. This file is
created in the destination folder that you specify in the Backup Site Server maintenance task properties.

 

Note: Configuration Manager can recover the site database from the Configuration Manager backup maintenance task or from a site database backup that you perform by using another process.
For example, you can restore the site database from a backup that is performed as part of a Microsoft SQL Server maintenance plan. Starting in Configuration Manager SP1, you can restore the site database from a backup that is performed by using System Center 2012 Data Protection Manager (DPM).
For more information, see Using Data Protection Manager to Back up Your Site Database

 

Configuration Manager supports neither the backup of secondary sites nor the test upgrade of a secondary site database.

Although the site database is shared between sites in a hierarchy, plan to test the database at each applicable site before you upgrade that site. If you use database replicas for management points at a primary site, disable replication before you create the backup of the site database.

 

Uninstall WADK 8.0 and install WADK 8.1:

To deploy an operating system, System Center 2012 R2 Configuration Manager uses Windows Assessment and Deployment Kit 8.1 instead of Windows Assessment and Deployment Kit 8.0.
Before you run Setup, on the site server and on each computer that runs an instance of the SMS Provider you must uninstall the Windows Assessment and Deployment Kit 8.0, and then download and install Windows Assessment and Deployment Kit 8.1.

More information here: http://technet.microsoft.com/en-us/library/gg682187.aspx

If you have other servers with the SMS Provider installed, you also need to uninstall Windows ADK 8.0 on these servers

 

You can only deploy Windows 8.1 from a site server that is running System Center 2012 R2 Configuration Manager.

You can only deploy Windows 8 from a site server that is running Configuration Manager SP1.

 

 

Configuration Manager version

Windows AIK or Windows ADK
  Version

Windows PE versions for boot images
  customizable from the Configuration Manager console

Supported Windows PE versions for
  boot images not customizable from the Configuration Manager console

System Center 2012
  Configuration Manager with no service pack

Windows AIK for Windows 7

Windows PE 3

None

System Center 2012
  Configuration Manager with SP1

Windows ADK for Windows 8

Windows PE 4

None

System Center 2012
  Configuration Manager with SP1 and cumulative update 2

Windows ADK for Windows 8

Windows PE 4

Windows PE 3.11

System Center 2012
  Configuration Manager with SP1 and cumulative update 3

Windows ADK for Windows 8

Windows PE 4

Windows PE 3.11 and
  Windows PE 5

System Center 2012 R2 Configuration
  Manager

Windows ADK for Windows 8.1

Windows PE 5

Windows PE 3.11

From <http://technet.microsoft.com/en-us/library/gg682187.aspx>

 

We only require to check the following features during the WADK8.1 installation wizard:

- Deployment Tools

- Windows PE

- USMT

 

Install critical windows updates to site servers and reboot (Primary, Secondaries). 
Restart the siteserver and each computer that hosts a site system role to ensure that there are no pending actions from a recent installation of updates or from prerequisites.
Check/monitor that all servers work as expected after the reboot and all services for CM12 are running.

 

- Make sure no maintenance tasks are running during upgrade.

- Run R2 setup prerequisites checker to verify the prerequisites, You may download the prerequisites from a machine and then copy them to the server.


In Windows Explorer, browse to one of the following locations:

<ConfigMgrInstallationMedia>\SMSSETUP\BIN\X64.
|<ConfigMgrInstallationPath>\BIN\X64.

Copy the following files to the destination folder on the other computer:
Prereqchk.exe
Prereqcore.dll
Basesql.dll
Basesvr.dll
Baseutil.dll

From http://technet.microsoft.com/en-us/library/b22fa03d-ad29-4a72-99d9-4c31bfa53f0f 
Check also: http://technet.microsoft.com/en-us/library/b22fa03d-ad29-4a72-99d9-4c31bfa53f0f#BKMK_SetupDownloader 

After you restore the site database, on the SQL Server computer, run Configuration Manager Setup from the Configuration Manager service pack media, with the /TESTDBUPGRADE command-line option.
It is not supported to run a test database upgrade on the production site database. Doing so upgrades the site database and could render your site inoperable. Also, do not restore the copy of the database that you use to test he database
upgrade to the same SQL Server that hosts the production database. This is because the same SQL Server Service Broker endpoints can be used by each copy of the database, and messages sent to the copy during the upgrade
test can be picked up by the production database, and vice versa

 

During a site upgrade, Configuration Manager automatically upgrades site system roles at the site by reinstalling each site system role. When prerequisites are not met, the site system role might not reinstall or might reinstall, but might fail to operate correctly.

 

Run the setup of Cm12 R2.

 

If you want to integrate MDT 2013, see here: http://blogs.technet.com/b/configmgrteam/archive/2013/10/21/microsoft-deployment-toolkit-2013-now-available.aspx
and here: http://technet.microsoft.com/en-us/library/dn744295.aspx and even here: http://social.technet.microsoft.com/Forums/en-US/d1e9d510-efa7-430b-892a-a9f9bfd2a223/integration-mdt2013-with-sccm2012-r2?forum=configmanagerdeployment

Verify OSD, Task sequences, boot images…

Upgrade consoles, secondaries from console, clients (via any method)

Reconfigure the database maintenance tasks you might have disabled prior to the upgrade.

 

If you want to install any CM12 R2 latest Service Pack/CU, then you will need to upgrade again the consoles, site servers, secondary servers, clients.

When you upgrade the top-level site of a hierarchy to a new service pack, the client installation package on each distribution point in the hierarchy is also updated. When you upgrade a primary site, the client upgrade package that is available from that primary site is updated.

 

*You may create a test VM and perform the below procedure, before applying it to the production environment, just to be confident with the whole sequence of steps...*