Okay so to start off, this game mode isn't randomized as far as I can tell(at least for the first 12 screens, after which there's just too many enemies to really count and my personal best is somewhere around room 15 with 19050).

The layout for the 12 screens that need to be cleared to get the achievement are as follows:
1st screen 3 bats 3 zombies
2nd screen 3 pistol 2 bat 4 zombies 2 pistol
3rd screen 2 zombie 3 pistol 4 bat 4 pistol 2 red shotgun
4th screen 4 red shotgun 4 zombie 4 pistol
5th screen 8 bats 4 smg 2 zombie
6th screen 18 zombies
7th screen 2 bat 2 zombie 2 pistol 2 red shotgun 2 smg 2 zombie 2 blue shotgun
8th screen 4 red shotgun 4 zombie 4 blue shotgun
9th screen 10 smg
10th screen 4 smg 4 bat 4 pistol 4 blue shotgun
11th screen 15? blue shotguns
12th screen giant bullet

The easiest way of clearing any room prior to 13 is to just kill each enemy as soon as they spawn. The only 3 rooms that aren't doable that way are 9, 11, and 12. For 9 and 11 circling the room and trying to pop off shots to eventually kill of the enemies while continually going around the outer edge of the room will work pretty well. 12 is what the achievement is referring to, the giant bullet does 3-4 stomps that release a circle of bullets outward from him, afterward he'll do a spiral bullet pattern which you'll need to dodge roll multiple lines of bullets at the end of which you can usually get a nice line of pistol(or if you're lucky an upgrade) shots into him. It usually takes between 2-3 spiral patterns to kill him if you're landing most of your pistol shots.

As for which upgrades I think are good in order of most to least useful are as follows(by the way you can reload these by dodge rolling enemy bullets for 5 rounds per each bullet dodge rolled through):
1. Rapid(Best if you're accurate and able to lock and unlock your aiming angle with some ease)
2. Spread(Best held down and fired instead of trying to make it last. You're also only getting 45 more pellets on in total ammo than rapid)
3. Pistol(Your starting gun which is pretty good on it's own and should be held down for rapid fire unless you need to change your aim)
4. "O"(Honestly I forgot what it was called because I avoid it at all costs. It's slower than your pistol and needs to be timed very well to do any real extra damage)