With my first couple of attempts at this, I found that I failed often because I couldn't track down the last few enemies on a level, and with the requirement for YAAM with this challenge, finding everyone within 5 minutes was a priority. I started opening with Intuition, and noticed a significant improvement in progress before death, so I just stuck with it.
Intuition naturally inclined me toward Cateye, and with AoMC this was doubly useful for finding all the enemies, and for staying out of harm's way.
Hellrunner was the next priority after MCe, since movement speed was the next major issue I faced with this challenge. Knowing where everyone is helps a lot and was the top priority, but with some level layouts I still struggled to get where I needed to go - especially levels with teleporters sending enemies back to areas I had previously cleared. I debated Finesse -> Juggler, but decided that movement time was a greater risk then firing and switching time combined, especially with MC helping out the damage output(meaning fewer trigger pulls per kill). After the first two levels of HR and the discovery of Phase boots, that was the next thing I addressed before finishing HR, and instant switches definitely helped while I was having ammo troubles - I was juggling a chaingun and a plasma rifle to conserve ammo and depending on what kind of target I was engaging, and being able to switch in zero time was definitely a plus both for safety and for level completion.
One more comment on the early game - reloading kills. My habit of automatically reloading after every engagement was very costly in terms of time, and I had to switch to a more controlled style where I only reloaded when I was empty, or down to the last burst or two in the magazine with a bigger enemy approaching. AoMC was also an immense help here, because most softer targets only took one burst to go down, and even bigger stuff like Knights went down in two, so not having a full magazine wasn't as much of an issue as it usually is for me. This is another area where I anticipate serious problems with QM Angelic - If I ever decide to try that, I'll definitely look into the gunrunner build.