You MUST be checked in no later than 1 hour before your scheduled departure time, so I would be sure to get in line no later than 1 hour before that (6:20pm.) Though to avoid any problems, I would get there as was previously stated no later than 5:45pm, meaning you need to be exiting the train no later than 5:30pm.
Just as a correction, Continemtal departs from Terminal C at EWR, not Terminal 3.
After exiting the train, you will go upstais into the Train Station. You will need to present your Amtrak Ticket Stub to the agent at the faregates to be permitted entry. If you lose your ticket, or your ticket does not list EWR as your destination it will cost you 5.50 to pass through the turnstiles.
Board the AirTrain (monorail) and take it to Terminal C. Exit the monorail, go downstairs into the terminal, and then go to the upper level to checkin. Once upstairs, Mumbai flights have a dedicated checkin counter, which should be to the left.