To win the Tag Team Championship, you need to be rank 3 of the Tag Team division and locked into a feud with the champion. The championship match should take place at the pay per view.
I'm not sure if either the NXT Tag Team Championships or the WWE Tag Team championships or both work for this achievement. I earned it by winning the WWE Tag Team championship.NOTE: xSpecial Movex was able to get the achievement by winning to NXT Tag Team titles, so it looks like both work.
You will automatically be given a tag team partner.
NOTE: You can begin a feud with the champions by doing a call out promo, going to the champions tab and selecting the current champion for your division. If you do this when you are rank 4 and win your match for the night you will move up to rank 3 and automatically qualify for a title shot.
Read this guide to figure out how to change divisions:
You can earn the following achievements the same way: