This is really a mystery for me. What is the "daily reputation cap" that is required to get Epic, Legendary, and Mortarboard badges?
You can earn a maximum of +200 reputation from upvotes and suggested edits in any given day. Accepted answers and bounties are counted separately (source). Reputation "lost" from the reputation cap is not awarded on following days.)
This is from the Reputation FAQ.
You can find out whether you've hit the reputation cap. Look here for instructions:
Make sure you are logged in, and visit
So at the end of the reputation report you find a section like this:
So for getting the badges you need to accumulate the right amount of days you hit 200+ reputation.