As you know, Team Foundation Server 2008 had several limitations which prevents a direct migration to 2012 or 2013. It is a legacy release, good at its times but definitely not adequate anymore.
Migrating it through an in-place upgrade to 2010 and then a move to 2012/2013 version (from now on modern) is feasible, but often the server where the legacy version runs is old as well – 32 bit only CPU overall – making the migration path harder because of the move.
There is a very handy tool for dealing with this scenario: TFSConfig Import.
It is meant to convert the legacy server into a new Team Project Collection in the modern instance. It won’t migrate reports or SharePoint, but it is worth using it as it saves a ton of time in the process.
It is needed to move the databases onto the current Team Foundation Server – or upgrade the legacy one to a supported version by the modern release you are using – and then launching the command as an administrator:
TFSConfig Import /SQLInstance:<servername> /CollectionName:<MigratedCollectionName> /confirmed
The /confirmed switch is meant to confirm you have backups of the databases you are converting, as after the process they won’t be compatible with the old TFS.