I want to thank you all for your replies, this way I can show to my boss just how wrong he is and tell him we're wasting a lot of time, thank you very much!

Lynn, in fact the way you say is how I do, first Upgrade Advisor, then fixing, then backup with fixes done, restore in the new server and change compatibility mode, though I'll do some research on side-by-side upgrade, as you and Grant have suggested.