Using the Warp beacon from The Royal Gadgets Pack DLC makes this achievement fairly easy. Like the other solutions note, you need to do it in one run, no resets for the achievement to pop.
Traverse level 3-4 normally without winding in the rope or crouch anchoring. When you reach a road block, travel without the chariot as far as you can go then press
to plant the beacon then
again to warp it. I went for the top exit and the only time the 'distance from chariot' countdown started was on the final ascent to the exit. A quick jump over to the last flat ledge on the left then mash
to get the chariot to warp in time was the only tricky part.
It takes 20 seconds for the ability to recharge so you'll occasionally have to wait a few times in a row.