I got the money and equipment needed for the first attempt. For context, I will explain my strategy in the blog.

To beat the Fight Caves, I must conserve my resources as much as possible.

Prayer is going to play an integral role in later waves, do I cannot just use it like normal. I must only turn my prayer on when I am about to get hit. This will reduce the amount of prayer that I use and my potions should last me until the final wave. I also need to stay still early on. This will conserve my stamina in game so I can make an escape when needed. I can safespot (a method in which you use range in an area where an enemy cannot attack you.) most early enemies, so this shouldn't be an issue.

I chose Italy Rock as my safespot for this attempt.

I was able to block off most melee monsters here, so I took no damage for the first six waves.
After that, the Ranging monster came out, which can attack me in the safespot. This wouldn't last long, as the ranger does leave at wave 15 and doesnt come back until wave 22.

The next few waves were fairly simple, the new big monster was the Meleer, so I could go back to safe spotting. At wave 22, the ranger and meleer are both in the same wave. I used the ranger as a barrier between me and the meleer. This worked very well, until I misclicked and got killed in one hit.