In Sandbox Mode there are 30 challenges in total; each requiring a certain amount of kills to unlock. Simply do the first 10. For bronze medals you should be able to get them without preparing much at all, while if you want gold you'll probably need to bring specific things with you.
For challenges requiring x number of kills bring some good weapons, explosives, shotgun, sledge hammer etc.
For PP challenges bring many combo weapons-the Boomstick works great using its hold X move. To get the Boomstick combo card you need to get gold on the first challenge available to you (right where you started Sandbox Mode)-I suggest bringing 2-3 grenades; throwing them in opposite directions at the zombies, as well as a shotgun or two to kill additional zombies. If your having trouble go down the elevator in the Palisades mall, head through the door at the end of the hall and grab the BFG, go back up and into the Palisades Maintenance room. Combine with the amplifier and create the Super BFG. You should have no problem getting the 40 kills with it.
For challenges requiring you to get from point A to point B just have a speed upgrade or two or bring a quickstep- for all ways to make follow link http://deadrising.wikia.com/wiki/Quickstep
DON"T waste time killing zombies, simply run past.
For challenges requiring you to get zombies in an area get firecrackers to attract zombies.
Those are the most common types of challenges, to get gold in them you will probably need to be a high level and have magazines that help you with the challenge. Example: a PP magazine for PP challenges.
Getting 10 bronze medals should be easier and quicker to do then actually unlocking them; which can be easily done with the SUV-SUV keys cost $2.5 million at the pawnshop across from it.
Use the Hacker combo weapon(computer case + flashlight) on slot machines and atms; or get the gambling magazines-1 palisades mall, top of grotto;2 Bennie Jacks BBQ shack in the Americana; and 3 in security box #304. You should be fine without number 3. (I've heard 3 isn't even available in Sandbox Mode but I can't confirm either way) Go to the Slot Ranch Casino with them and keep playing the giant slot machine until you have enough money.
Let me know if i'm missing anything and good luck.