Considering the requirements of the other achievements in this game, it is quite likely that you will easily pass 5, 15, and 30 hours of play time while working towards the other achievements. However, if you would like to get the time achievements early, it is fairly easy.
Setup your computer's power setting so that it doesn't go to Sleep or Hibernate during period of inactivity. Disable the screen saver as well.
Once your computer is ready, load up any level and walk away. Make sure that no menus are up and you are just waiting to shoot the birds. When you come back, shoot the birds to end the level and whether you pass or fail the time will be added to your total. If you have passed 5, 15, or 30 hours while you are away, the achievement will unlock after completion of the level you left running.
This strategy works for the following achievements as well: