To win the NXT Championship, you need to be rank 3 of the NXT division and locked into a feud with the champion. The championship match should take place at the pay per view.
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: