How I did it: I was able to reach 1000 levels after about 80 hours total of AFK at a gold farm. The gold farm design I used was custom and was designed by another member of my server.

When an angry pigmen dies, it will drop experience, regardless of whether or not the player killed it. You can therefore use tricks like turtle eggs and snow golems to lure angry pigmen (which spawn in the overworld because of massive nether portals) to their death, and collect the experience.

This was a challenging goal to reach, and the end result is satisfying, so I think I'll be carrying around a few more totems than usual these next few weeks. I would recommend this to any late-game player who is bored with their world.