To clarify, AGM now requires level 35 I believe to start the quest.
The Defending Champion heirloom is BoA and is added to your heirlooms tab regardless of what toon you get it on. Its a very good trinket at 19 - almost always BiS. You earn it by opening the chest on a character you've gotten AGM on. So you can take your 120 and get the AGM by winning 12 chests. And then open a 13th one to get the BoA.
If any character already has AGM, including ones under level 35 - then they already have the achievement and can open the chest to get the BoA.
There is an identical BoA trinket called Returning Champion that is from the DMF chest if you already have that on a high level. You can also get and use 1 of each - which is often one of the BiS trinket combinations (depending on if your class/spec prefers int, insignia, or has GFd AGM).
Finally, I don't know whether RP realms are truly separate and if no one attempts to go for the chest - but you could start death knight or level a rogue/druid to 35+ for stealth in order to try and obtain it there. No clue how uncontested it will really be.