During the 2nd act you will get a mission from Yuri about a mystery box on a roof. Starting the mission unlocks Taskmaster’s bomb and drone challenges. Completing a couple of them will unlock the stealth and combat challenges. I first completed one drone and one bomb challenge. That’s when the other 2 types unlocked for me. Not sure if it’s completing one of each or simply completing 2 total challenges that unlocks the later types. The combat is by far the easiest to get spectacular on compared to the others. I consistently got double or more of the spectacular requirements without even trying very hard on the 1st try every time.