You will need to beat the Act III boss on Normal and Inferno difficulty for these two achievements. During this time, you will also want to do the challenges for Azmodone, all of which are possible on at least Hell difficulty.
No Reinforcements - Destroy the Demon Gates before any Demon Troopers can spawn while fighting Azmodan on Hell difficulty or higher
Hot Foot - Kill Azmodan without walking over the bloody demonic groun on Hell difficulty or higher
Be Cool - Kill Azmodan without getting hit by a fireball on Hell difficulty or higher
Azmodan Adds - Kill Azmodan without killing any of his minions on Hell difficulty or higher