A note: Your private key is bundled with your public key in your key pair, hence losing your private key and losing your key pair means exactly the same.
There is no way to recover your passphrase: your only hope is to try to remember what it was. If you don't succeed, you lose the use of your private key, and hence your whole key pair is now useless.
There is no way to recover your private key, either. It cannot be obtained from your public key or from any message that was signed/encrypted by that private key. You can only recover it if you made a backup in the past.
Hence, losing the passphrase or the key is definitive. If you generated a revocation certificate (and you should have), use it to revoke the key pair. You must also generate a new key pair, send the new public key to your contacts and warn them not to use the old public key any more.
Messages that were sent to you encrypted with the old key cannot be decrypted any more. Messages that were signed by you with the old key can still be verified by the recipients by using the old (revoked) key.
To avoid this disaster, it is recommended that you backup in advance your key pair: from Key Management, select File → Export Keys to File, make sure you included the secret key, then store the file in a safe place. Make sure you chose a passphrase you can remember, too.