I strugle to complete the challenges.
I just play without trying to complete them. When one pops up, I may focus a little more, but just playing a lot and exploring will get you a lot of them as you take all the characters from Normal to Ultimate mode.
If you really want to go after particular challenges (either for the achievement or to prestige your character) this guide has some good suggestions for strategies:
But I’d only do that if you specifically want to farm the challenges for BAR - like @Isthiswill, I normally pay very little attention while playing (and then have 5 or 6 points to spend at once!)