Eliminate the Act I final boss - The Butcher - while accomplishing certain tasks during the fight. They can be done over as many playthroughs as you want
Don't Stand in the Fire - Kill the Butcher without being burned by floor fires or being grabbed by Ancient Spear on Hell Difficulty or Higher
This is best paired with A Brief Butchering, or a fast kill on a lower difficulty, because you will need to stay close to him to avoid being pulled in by his Scorpion-like chain whip that he will throw at you to pull you into melee range if you're too far away. Staying close to him also means you will need to work to avoid the fire that comes out of the grates on the floor, and being fast helps offset the fear of being hit by the fire because the longer the fight lasts, the more fire will come out of the ground at a given time (so fast feet = little to worry about if you stay close to the boss).
A Brief Butchering - Kill the Butcher in under 2 minutes on Inferno difficulty
In order to do this you will want to have a decent set of gear, and a coop friend (or three) to both help do damage, and also allow you to go all-out damage without the fear of being forced to restart if you die.
Stunning Reversal - Kill the Butcher while he is stunned by his own charge attack on Nightmare difficulty or higher
One of The Butcher's attacks is a forward charge, which is pretty easy to spot and avoid as he will sort of glow just prior to doing it. The Butcher will charge forward, and once he hits a wall/the edge of his little arena, he will be briefly stunned. Be sure to finish him off while he is stunned to finish the challenge.