Can I fulfil the mitzvah of hearing the megillah by listening it by phone, or on the radio, TV, or any other electronic device? I’m working the night shift at a hospital, and can’t take off time to go to the synagogue to hear it.
No, hearing the megillah by any electronic means, by phone, or even via loudspeaker does not fulfil the mitzvah.
In your case, if you can’t find someone to fill in for you long enough to go to the synagogue, try to get someone to read it to you in person at the hospital. If that’s not possible, you yourself should read it from a scroll. If that’s not possible, read it from any written megillah but don’t recite the blessings.