Imago has 38 missiles worth of health. In almost every category you'll find yourself entering this fight with 4 super missiles, which means you need 18 more regular missiles to finish it off.
The fight starts when you destroy the left-most egg sac in the room. The background music will pause for a moment before starting up the boss music. As soon as the boss music starts is when you can start firing super missiles straight up and get 3 or 4 into Imago to start the fight. You want to left him bonk you to the left as he enters the room, run off the platform onto the ground, pause for just a moment to let Imago get going and then chase him downhill while firing missiles at him. With this setup you can easily defeat Imago in one round, although if you mess up the setup you may need to chase him back to the left to get him going downhill again.