So this achievement can take a while to get, mainly because is not easy to balance a ship without using hover blocks of any kind and it will take a few hours for you to design a chopper or aircraft stable enough to finish the whole circuit in one go without crashing or hitting something.

Fear not, I will share with you a workshop ship I made just for this as well as some instructions.

First, go to the steam workshop and subscribe to my creation, either follow this link:
https://steamhost.cn/steamcommunity_com/sharedfiles/filedetails/?id=2066327662

Or you can search for it yourself. Its named "Armed Stable Chopper" its a BetterFuture Aircraft.

So here are the steps:

1) After subscribing to my aircraft from the workshop and restarting the game (if it was open before) open the game and go to "New game"
2) Select "Gauntlet" and then "Home run"
3) Once loaded in, go to the "Load tech" section and then select the "Armed Stable Chopper"
4) Increase the speed of the helicopter rotors (using the arrow keys by default) up to "21.0", this is the value that is ideal for the chopper to almost float.
5) You will need to fine tune your rotors speed during the track to elevate and avoid obstacles and follow the terrain or lower the ship to pass through the checkpoints, I recommend "23.0" for slight elevations, "19.0" for slight declines.
6) The ship has ion drives and adjustment thrusters, as well as gyroscopes to make it easier to handle, with a bit of practice you should be able to finish the circuit without hitting any obstacle or the ground.
7) If you hit something or crash, simply press the escape key and choose to restart the gauntlet challenge until done.

Good luck.