This guide is for chrome users.
I am using this solution right now so I can confirm that it works.
Step one: Download the "Reverse Youtube Playlist" chrome add-on. [The add-on was last updated in 2014, but if you follow these steps it will still work]
Step two: Go to the youtube playlist that you want to reverse and add this to the end of the URL: &disable_polymer=true.
So your complete URL should look something like this: //www.youtube.com/watch?v=M1nd8WPZO_c&list=PL34C1F26D03F5F9B8&index=94&disable_polymer=true
Step three: The playlist bar should now look slightly different. You will also notice that there is an extra button on the playlist bar with a down and up arrow. This is the button to reverse the playlist using the add-on you downloaded earlier.
Clicking this button should reverse the current order of the playlist. The reason you need to add the text to the URL is because the add-on only works if you are using the old version of youtube.
If youtube decides to take away the old version this solution might stop working.
That is the solution. Enjoy