You don't need to completely remove the cover just to change the air filter.
To remove the cover you first need to remove the air filter and carrier just like you already have done.
Then, go to the front of the car and look down the gap between the hood an bumper cover. You will see two studs that connect the cover to the car body. These studs have rubber grommets in them to help hold the cover secure. You need to pry the bottom of the cover off these studs; it will be a little stiff, so don't be afraid to use a little muscle. Once you've got the cover off the studs, then go to the backside of the hood and pull up and to the rear to remove the cover; you'll have to twist, jiggle, and pull to get it out; again, don't be afraid you use a little muscle to do this.
Here are a couple of pics showing where these studs are: