Outside the range of what is normally considered believable.
It was Shakespeare who first used the word 'beyond' in a general 'outside the range of' sense, as opposed to its original 'at a great distance' meaning. This usage is found in Julius Caesar, 1601:
These things are beyond all use.
In The Tempest, 1610, he also extended usage to the 'unbelievable' meaning that is the 'beyond' of 'beyond belief':
Which is indeed almost beyond credit.
None of Shakespeare's works includes the expression 'beyond belief'; for that we have to wait a few years. John Gower's 1616 translation of the Latin poem Festivalls by Ovid (Publius Ovidius Naso) includes the first example of 'beyond belief' that I can find in print:
Nor could I dream that death purgu'd her grief.
Ah me! her courage was beyond belief.
See other phrases and sayings from Shakespeare.