I've advised elsewhere that the best way to get the kills award is to farm enemies in the end boss room, ideally while using the mummy's scepter as your weapon.
The gold one you will definitely get if you make a city of gold run and bring bunch of bombs with you, but in my opinion that's harder than the challenge itself. Just try to collect as many items (especially bombs) as possible, and take your time getting everything you can in each level.
The time one is what I consider to be the hardest one. Just book it, don't go for any gold or any powerups that will take you more than a few seconds to obtain. It's possible to reach the jungle area in under 1 minute if you get a halfway decent layout and don't let anything distract you.