How to Do Tun's Challenges with the True Crown - Spelunky 2 Science

A few facts:
If the Tun challenge spawns in 2-4 and you already have the True Crown, you would have to anger Tun to get the Hou Yi Bow, which is crucial for reaching the Cosmic Ocean.
To get forgiven by Tun, you need to kill her three times: in 2-4, 4-1, and 4-2. She never spawns in 3-1.
Unfortunately, it’s impossible to get forgiven by her before 4-2 if you want the Elixir or Clone Gun.
In that situation, you would want to get the bow without angering her. This video shows how to do it.
These techniques shine in 4-player COOP since only one player gets infinite bombs, leaving the Clone Gun and the bag with 24 ropes and bombs for others.
Also, the extra hands help a lot in carrying more items, meaning more of these strategies are possible in a single run.