It's a simple idea of taking the lead bird and trying to get the other birds that are "lost" into the flock. You have to avoid many different flying objects (i.e. planes and ufos) or your flock diminishes with each bord that gets hit. If you keep a flock of 16 birds you get bonus points for each extra bird that comes to your flock. You can do upgrades to make the game easier to get the achievements, although, the Sky Captain achievement is the most difficult. You'll ultimately be racing your flock all over the screen to avoid getting hit around 100+ seconds into the game. "Frustrating" should have been part of the title for this game at that point since I still haven't gotten to 180 seconds yet.

Also, should you only have the lead bird and get hit by a plane or such, you will have to start over unless you get the upgrade "Pheonix Pendant" that allows you three lives and/or the "Poseidon's Blessing" that makes the lead bird invulnerable over oceans. While these two upgrades are nice, the other upgrades are needed to speed up your bird, increase the size of the circle you capture birds into the flock, make weather not slow you down, increase the number of birds available, etc. I recommend you start with the Royal Lineage upgrade to get the flock of 16 Swans for the Borgeoisie achievement out of the way. If you get the Homing Beacon before that, it will make it more difficult to avoid regular geese when trying to get the Swans. However, you can reset the upgrades and repurchase them in any order you want without penalty for the reset. This way if you got Homing Beacon first, you can go back and set up your birds how you need for any achievement.