I suck at this game all I do is die and respawn and keep going LOL. Quests are absolutely doable though, couple hours from scratch not too bad. The car made me lol, it flips over and explodes immediately.
What Psycho says is correct, the quest (mission in game) has to appear in game and only after completing it then will the quest be awarded, the med pack one doesn't show up until over halfway through the game IIRC, the bomberman one should show up early. It really is a nuisance though, I'm pretty sure I found 6 bronze chests before I got the mission in game, then I had to find 6 more >.
At Start ... Run.. type that: %appdata% then go to /Macromedia/Flash Player/ #Shared Objects / ????? / cache.armorgames.com / zombotron_save1.sol and delete the sol file.
Trophy Hunter means what? you got to do all the missions or to get all that stuff that upgrades you?