Hi Louise
The problem you have is that while Continuous Service was introduced in 1853, it did not become compulsory until 1873. So if your man did not sign up, and left the navy prior to 1873, then there will not be an online record for him.
I'm afraid that your only option is to visit the National Archives and look at the Ships Description Book for HMS Megaera (ADM 38/8537). This will provide a physical description of your man, information on place of birth, place of usual residency, marital status, and a list of all the ships he had served on to that point.
Martin