1. Install the Update Installer version 7.x as it will be needed for latest fix packs for v 6.1.x. More details at:
http://www-01.ibm.com/support/docview.wss?rs=180&uid=swg24020447
2. Download all the pack files (.pak) that you need to upgrade. If you are not sure then download all.
http://www-01.ibm.com/support/docview.wss?rs=180&uid=swg24022255
3. Copy the fix pack files to the maintenance folder under Update Installer install location.
4. Run Update installer and point it to the maintenance folder.
5. You will have to run the update installer multiple times to upgrade WAS, IHS, EJB3 Feature pack, IHS Plugin etc one by one.
I have upgraded several times without any issues.