The parade had been gigantic and gaudy, and the next morning the New York Sun, more reliable than the paper of record (it wasn’t sponsoring the expedition), declared halfheartedly that it had been “fine enough.” It would have been impossible to live up to the hype.

'not to live up to the hype' = (of sth advertised) not to be as good/wonderful as the hype (publicity) had said it was/was going to be.

'it would have been impossible [for the parade] to live up to the hype [created about it beforehand by the advertisers]' = it would have been impossible for it to be as wonderful as [the organisers/advertisers] had suggested it would be.

In other words, the parade was guaranteed to be disappointing because the publicity about it beforehand had been so exaggerated.

to live up to expectations = to meet/satisfy one's expectations.
to live up to one's promise = to fulfill a promise one's made.

* 'We were told the restaurant was the best in town and it lived up to our expectations'.
* 'He's promised to repay the money, but unfortunately he has no intention of living up to his promise'.