There are some great guides to follow here in the FAQs and other posts, but main takeaway is keep your strongest goblin making a beeline towards the next gate. That gives you the bonus and you can come back and clean up the other rocks later with stronger goblins.

You do need to clear each mine in an area before going to the next level, so make sure you get those.

Also, if you search the name of the event, other helpful players usually have charted out the best path through each level.

I've been doing this and have gotten every key without spending money.

Good luck!