How many Stars do I need to complete the story

There's a star you can only earn after getting a message at the Mailtoad from one of the robots with the gear heads. After that you'll be able to meet him in the galaxy, he'll want you to lure a Gooma over to him. So, I guess keep playing and come back later.

There are a total of 242 stars:

• 120 standard Gold stars, consisting of:
  • 56 Power stars (the normal ones)
  • 6 Grand Stars (at the end of each world)
  • 17 Hidden Stars (in 17 different galaxies)
  • 29 Comet Stars (in 29 different galaxies)
  • 6 Additional Normal Stars after beating the game for the first time.
  • 6 Additional Comet Stars after beating the game for the first time.
• 120 Green Stars which appear after you collected the first 120 yellow stars and have beaten the game again (2 or 3 per galaxy, 18 per world, except for the very last world, which has 12)
• 2 additional Gold stars after you have collected all the previous 240 stars. (1 Power Star, 1 Comet Star, which also requires 9999 Starbits)

The only way to get all Comet Stars, is to collect all Comet Coins, which are found on the first level of each galaxy, including the very last one!

Note that it is possible to get Bronze Stars instead of Gold Stars if you use the Cosmic Guide available (after dying a couple of times) on certain levels (available in every galaxy, but not every level). While these Bronze Stars allow you to continue to move on, the do not count with respect to unlocking certain secrets.