Awesome Ways to Show Off

Once you've become a Grandmaster, there are plenty of ways to enjoy yourself as a Monk in Heroic-level quests.

Not only would completing quests and raids listed here with limited resources is quite fun, but it also verifies the integrity of your Monk's build and gameplay--or exposes any significant weaknesses for you to resolve later, especially as you enter Epic difficulty quests and raids.

Most importantly, you'll push your fighting skill to the maximum, using everything you know and everything you have. Survive any one of these and know that you will bring great honor to your dojo--as well as be able to sneer at non-monastics who claim that Monks are only good for stuns and "party support." (Do we look like we're carrying hors d'oeuvres and cake?)

Here's a list that I hope will expand as more students submit their suggestions.

Enter the "Tempest Spine" raid on Heroic Elite and complete it, alone. You'll likely need an INT helmet and a way to open a lock or two.
Complete "Devil's Assault", Heroic Elite, alone. Then become an Epic character and try Epic Normal and Hard. Try Epic Elite alone if you want to commit suicide.
Complete "Frame Work", assassinating the chief, hopefully grabbing your loot and escaping in under 5 minutes. Stealth and speed are needed, as well as knowing where two ballistas fire.
Slay 1,500 denizens on the Devil Battlefield.
Participate in a mostly-Monk run on "The Shroud" (with 2 healers). Everybody was kung-fu fighting!
Complete all four Shroud flagging runs alone. Of these, "Let Sleeping Dust Lie" can hallmark a Ninja Spy's pinpoint assassination skills while "Running with the Devils" and "Ritual Sacrifice" require powerful attacks to defend NPCs.
Take on the Devourer of Dreams in "The Dreaming Dark," alone, on Heroic Casual or better (he's rather nasty with stat-draining damage and stunning).
Enter "Invaders!" and destroy every single beholder on Elite difficulty. You may use Fergus, a Level 8 hireling, for Restoration spells, and no one else. Collect Outsider Tokens for a special treat.
Complete "Blockade Buster" without being detected and/or with less than 10 kills. The quest is specifically designed so not to break stealth when entering doors.
Complete "Maraud the Mines" with less than 15 kills and without any archers detecting you, alone.
Complete any one (or more) of the Sharavath flagging quests for "Tower of Despair," alone. "Genesis Point" is harder to solo, but technically doable with a hireling and high graphic settings.
Complete "The Chronoscope," alone, on Heroic Elite difficulty. Then go Epic.
Complete the raid "Zawabi's Revenge" (the final battle against the Demon Queen herself) on Heroic Normal, alone. (This may be the most difficult since ranged ability for you is limited as a non-Epic character.)
Go find your Icy Raiment outfit. It's in Garamol's chest, deep in The Subterrane. It's a raid wilderness, so going alone is required. And then, once you survive the skeleton giants, the beholders and renders, there's the traps that line the cylindrical lair above the red-named skeleton giant. Hopefully you won't spawn too many of his minions...
Complete the Reaver's Refuge flagging quests. "Prey on the Hunter" is most challenging, alone, so a summoned distraction or two may be needed.
...And then run "Stealer of Souls" and get your Dragontouched Vestments. Are you up to destroying the undead Sor'jek yourself?
Run every quest in Elite difficulty and unlock House Favor.
Defeat everything alone in "The Weapons Shipment." You can bring along a Cleric hireling at the start to keep the zerging Planescaller alive to the field entrance. But it's going to die a quick death on the field, and only your monastic prowess will save you from a respawning horde of angry, powerful enemies.