Some old classics I remember people suggesting back on Turtle
No map challenge. No world map, no zone map. No maps at all. You have to rely on your knowledge of the game to make your way around
Victory or Death challenge. Once you lock into combat, you either win, or you commit seppuku after running from the battlefield in a shameful display. (Would be extra dangerous on HC mode for obvious reasons.)
Monster Hunter Challenge. You get a list of dangerous rares and big bad elite mobs in zones. You have to go slay these rares before a certain level, or you fail the challenge. Each level tier adds a new list. So, 1 - 10 - 10 - 20 would have a list and then 30 - 40 have a list and then 50 - 60 have a list
Treasure hunter challenge. Open every chest you see. Fish every wreckage. Mine or gather every node encountered.
Dungeon Siege Challenge. You have to clear out each dungeon while leveling up.
The Random Talent Challenge. You don't get a choice about your talents on this challenge. A random talent will be picked for you while leveling up. Alternatively, or also, a talentless challenge, no talents are available.
Season Challenge. In snow zones, you take damage if dressed too skimpy, better dress warmly, in hot zones, you die if dressed too warmly, better dress down, Swampy zones, you get infected with poison and diseases, have cures ready!
The collector challenge. You have to keep everything that you find while leveling up. EVERYTHING. By level 60 you'll have an enormous museum in your bank.
Roll the dice challenge. Every five levels, you have to roll the dice. Either a great boon or a great plague befalls you. All money deleted, Weapon destroyed. Talents randomly switched. Change zone instantly. But boons could be like, double your money, a better version of your current weapon. *Shrug* Many possibilities.