there's no exact pre-requisite for the emblems since there's many factors which affect them. I had the same problem as you for a while and what I heard is that a 40 kill to death ratio is needed to get the skull emblem. when I had around that one day I just got it. they say in addition reviving other players, accuracy and downs is important too. if you look hard enough on this forum (under the zombie section) theres actually a group of people who compiled everyone who submitted their stats and associated emblem to provide averages for the different emblems.
My suggestion to you is play custom zombies matches on easy as it still affects stats the same way public or custom normal difficulty does but obviously its easier. and play a map you're comfortable with. I always found that Die Rise is a great map to do so on since the pack-a-punch machine is a available as soon as power is turned on. If you're going solo in custom games make sure to pick up quick revive first as it will automatically revive you if you accidentally do something stupid in the early rounds. I found once I had Jug, speed cola, quick revive, and mule kick and pack-a-punched both guns and built the sliquifier as the third weapon an I'd just camp up on the rooftop until round 25-26 fairly easily. you can really use the sliquifier to slow down zombies in the later rounds. I wouldnt get Whos Who though as I've noticed itd glitch out if i didnt revive myself even if I had quick revive too (on solo). Also iIf you build the trample steam and run around it when the jumping jacks come and let the trample steam kill them you should get a free perk. it may help you with you point budgeting. My last suggestion is once you've achieved a certain kill ratio or whatever 150 kills+ etc or feel like you might not last much longer I would bank any excess point you have. then youll be able to pick em up in the next match to get off to a decent start. cheers.