for level 45 pushback, vulcan cannon worked for me, i also had med-high luck for the powerups. A single ability recharge drop keeps you alive for a minute using all your pushbacks and picking the powerup, and pushback separates the runners pretty well. I actually completed the level with deadly shield, health regen and piercing bullets but i never regen a sec, u can use whatever u fancy.
challenge 5: shutdown coal plant, 2 nuclear plants, lab, 3 metal mines and an oil tower. one more nuclear plant, updgrade nuclears as soon as u have 100 research points, nuclear dump, factory, 1 engineer, few garbage trucks and a dump, change vehicles to consume gas. 1st evening comes, alternate gun towers and those reflectors (d-1), build where they attack. u should survive (oil plant falls but have enough gas for the game), if u can upgrade recycle plant u wont run out of metal either. u'll have 0 smog at the second evening, so u can pretty much do anything, make a lot of garbage trucks - you need to recycle zombie parts for a positive score, make some labs, upgrade everything you use. You'll need some farms too. The shape of your base might count the first evening, be sure to not build a lot of things around the fortress, so you can place a lot of defenses around it.
so the autosave is unclear, for the easy badge i had to start a new game yesterday, and i'd have to play through the whole thing again to get the hard badge today.
 "Zombie Madness"){kind=icon}
 "Super Energy Apocalypse : RECYCLED!"){kind=icon}
 "Fancy Pants Adventure: World 2"){kind=icon}
 "Cargo Bridge"){kind=icon}
 "Scriball"){kind=icon}
 "Bubble Tanks"){kind=icon}
 "Trigger Knight"){kind=icon}
 "Road Wolves"){kind=icon}
 "Survival Lab"){kind=icon}
 "Obliterate Everything"){kind=icon}
 "Town of Fears"){kind=icon}
 "XenoSquad"){kind=icon}
 "Georganism"){kind=icon}
 "BasketBalls"){kind=icon}
 "Fortress Magnus"){kind=icon}
 "Frantic Frigates"){kind=icon}
 "Sports Heads: Football"){kind=icon}