It's true that it's not possible to test any mods outside of the skills and drills section -- most browsers no longer support the old simulator's core plugin unfortunately. Eventually those badges will be moved into the vox-l simulator (the new simulator) -- not sure when. Meanwhile, it should still be possible to test the avengers and other badges in minecraft no matter what browser you're using.
If you're unable to run the avengers mod, after following my tips earlier (a few comments ago), please let me know so I can help troubleshoot further. And if you can't run any mods at all, definitely let me know.