Proper punctuation for a long sentence

Solution 1:

The basic sentence is I'm no genius, but I'm no fool either. The 'pause' comma is not essential but it aids reading.

my grade cards can tell you is an aside, and is thus in parenthesis - the offsetting commas are required.

The em-dash is always a safe bet to replace a conjunction or a colon.

I'm no genius, my grade cards can tell you that, but I'm no fool either—speaking to me will tell you that.

Solution 2:

Your original sentence: I'm no genius, my grade cards can tell you that; but I'm no fool either, speaking to me will tell you that.

Not bad, but the commas after "genius" and "either" are not optimal.

Your rewrite: I'm no genius - my grade cards can tell you that, but I'm no fool either - speaking to me will tell you that.

The dashes are definitely better and may be the best you can do with this sentence structure, but you may want to consider using a semicolon after the first "that", as you did in your original sentence:

I'm no genius - my grade cards can tell you that; but I'm no fool either - speaking to me will tell you that.

You could also consider dropping "but".

If you're interested in more of a rewrite, you might consider:

My grade cards may tell you I'm no genius, but speaking to me will tell you I'm no fool.

Good rhythm. Nice way to contrast the difference between what you grade cards say and what speaking with you would say.