just completed hard badge. in my opinion best levels for getting the 20 a ranks are: 1-16, 19, bonus level 1+2 & survival. what yashainu said isn't true! you DON'T have to complete A rank on stage 20 for unlocking bonus stage 4!
just got the impossible badge! needed 6 tries on epic. you MUST HAVE the defender ability in order to beat the final boss! matt has to defend a lot on the final battle (stone edge equipped), let the girl cast heal more/slime bunny/barrier and revive (autolife) AND seal the special ability of the nazi with syphon! the rest is a lot of counterattacks/aerial support & cat warrior ;-)
finished hard badge! when you have problems completing level 17 challenge just kill everyone except one or 2 gunners. turn on slow motion when energy is full. while they shoot at you just dash to them (ANTI BULLET FIELD HAS TO BE EQUIPPED) and THEN IMMEDIATELY TELEPORT AWAY so that they can't shoot immediately the next bullets at you. then wait a second or so (just that you can use the dash again) and then again dash to them and teleport away... works 100%