well it's hard to say what can be the ultimate challange for you, as I don't know what is your playing stile nor which is your policy about exploiting game mechanics, or what you consider to be a challange successfully completed (i.e. you go with standard victory conditions from TW games? you play with lore or history accurancy? etc).
I don't know of any "impossible" task in TATW, but at any rate I can tell you what I consider a very HARD task
Use MOS, play as Gondor and activate all the scripts spamming extra armies for Mordor (there should be more than one script in the last MOS release); don't need to say of course to play VH/VH, don't exploit bad AI and so on and you should be put on hard test against a continuos flow of troops, to which you'll see more added from Harad and possibly much more from all the evil factions when you'll be object of an Invasion called by Sauron.
Though it depends on variuos things, it won't be impossible to see up to 10 Harad stacks pushing towards Gondor and usually 5-6 from Mordor (speaking about mid to late campaign), plus possibly some from Isengard and all the other guys running at you during invasions.
At any rate, conquering the whole ME with any faction (Mordor excluded I believe) is a very hard task, 'cause all the main settlements have Garrison Script and when you leave your side (good-bad) to fight against the whole world .. well the whole world turns against you
I don't know how much you know about TATW and its submods, but as a general rule there are MANY different features you shold know of before deciding what is hard for you