This one is so hard, but I found out that making food your priority pick-up is the key (since there's no darned tree!). For instance if you just had some stone drop, but the food is going to drop in a couple of seconds wait for the food. Pick that up, then go get the stone. I noticed that I always had at least 20 or 30 of all the other supplies left at the end, but only 3 food, so you aren't hurting yourself by waiting those few seconds for the food.
I'm not very good at writing out how I did things, so you'll have to give me a break on it, but this is what I did (except when I panic and start clicking on anything that's available

):
Food and upgrade it - Build the Quarry - Clear the garlic on the path to the wood
Sawmill and upgrade it - Clear to Iron and mine the center gold pile
Clear the left garlic and the large rock - Build the Iron and start working towards the forge
Upgrade the Quarry and then the Iron - Build the Forge and upgrade it
Use the 'upgrade all buildings' icon
Finish clearing to the pool and Handyman - Build the Handyman
Clear the trap blocking the pool - Repair the pool and talk to the Mermaid
Clear the far left path while you - Remove the large rock at the center bottom
Remove the far left trap
Remove the other large rock at the center bottom - Build the left bridge and grab the bomb
Build the other bottom bridge (the one to the bottom right) and remove the trap
At this point I just try to do whatever is available, but have found it's better to pick up the barbells starting at the far left because it takes him longer to get there. Also make sure you have enough gold to get the barbells. If I remember right each barbell takes 20 gold to pick up so you'll need a total of 60 gold to get all 3 of them.
Build the gym and give the barbells to the giant while you're building the last bridge (the one that leads to the maze).
Hope this helps, and honestly I'm not so sure it matters exactly what order you clear in because I've done it with 3-stars several different ways. The big thing is to stay on picking up the food. Anyway, hope this helps and good luck!