Minimally, you want your webserver to be able to write to the files in your data directory (files_dir) and your “public” and “cache” directories, and you want to deny the ability to write to everything else. If you want to be able to add, remove, and update plugins over the web, you will also need your “plugins” directory to be writable.
See:
You will get different errors in each step and it is easy to fix each part of errors on each step.
Also, upgrade to 3.1.2 oficially (am i right?) supported only from the last 2.4.8 version.
And 777 is not a very good way. Not all files should be executable, for example. It is very strange, that webserver (cpanel application) does not have permissions to the wwwroot, or console php in web hosting have different permissions than cpanel.
And one more question. There is your “files” dir stored? Is it in wwwroot?
The upgrade to 3.1.2 is supported from any 2.4.x installation. Versions earlier than 2.4.0 are unsupported.