First things first, this is NOT EASY. This took me about 75 tries, even though I have a lot of experience with this game. But, here's some tips I've put together to help...
-Stay on the main path. If there's a crate or the damsel is somewhere off the path, don't go for it. You could pick up some gold by accident, and it wastes time, which leads me onto my second tip...
-Beat the levels as fast as possible. If you can beat a level within 20 seconds or less, you will not get a dark level, which can ruin your run easily. If you do run into a dark level, take it extra slow, and make sure to throw your torch down a pit before you venture down there.
-Get the Udjat Eye, only if its relatively safe to get. The Udjat Eye isn't essential, but it'll make you be able to see gems in the walls. This can help you when you are blowing up a wall, so you know exactly where any loose gems are in a wall. It will also help with Olmec, for the reasons I just stated. And speaking of blowing things up...
-Use your bombs carefully. If you decide to plant a bomb, when it explodes gold and gems could go flying everywhere, so get some cover as soon as you plant that bomb. And also, save your bombs and ropes too. You WILL need them for the Olmec fight.
-Don't rob the shops. Now normally, I'd encourage you to rob them, but considering you have to be fast so you don't get dark levels, and the shopkeeper will drop some gold when killed, I can't recommend it. You're not going to need anything he sells, so just rely on crates that you'll come across.
-With Olmec, lure him to the far side of the arena, and find a spot where there's not much treasure in the ground. From there you should place a bomb in the middle of two blocks so it creates a 4-block wide hole, then repeat all the way down. Use your ropes continuously to avoid treasure, and climb to the top of the arena if you need more supplies.
-I know this last one is kind of obvious, but remember, YOU CAN WHIP TREASURE OUT OF YOUR WAY! Seriously, this is the most important tip for this, and without it it would be near impossible.
Thanks for reading, and I hope this guide will help you grab this stupid achievement.