For the quickest solution, download and run this jarfix.exe application from their website and you should be able to open the TRiBot_Loader.jar and run the TRiBot client with no issues. (thanks to @erickho123 )
If for whatever reason you are unable to download or execute the jarfix application, follow this step-by-step tutorial to open the TRiBot_Loader using the correct version of java:
Right-click the TRiBot_Loader.jar file.
Select the "Open with..." option from the drop-down menu.
Click on the "Browse" option marked with the red box:
Paste this into the address bar at the top to navigate directly to the Java folder we need:
C:\Program Files (x86)\Java\jdk1.8.0_73\jre\bin
*this part may need to be edited to reflect your current java version
Once there, find the "javaw.exe" Application and then click "Open"
Note: You must have java installed before you are able to use TRiBot!
If you do not have java installed, download it from the Oracle website.