If you earned a badge on a deleted question, you click on that badge you earned (in my example, it was Nice Answer), you'll see the link to the deleted answer. Click that link and you'll get the oops page.
Test it on my Nice Answer badge HERE (the bottom one in that list is deleted).
I guess the fixes would be either:
1) Don't show deleted questions on there at all (consistent with the rest of the site).
2) Show it, but don't have it as a link, just maybe put [deleted] beside it, something like:
I'd go for number 1.