From Disc Two's main menu, go to "Data Console". Once in, highlight "Main Menu" and press right. A red light will now appear on the computer. Press enter. The spaceship will now move, and the access code "7-4-Enter" will now appear on the computer screen. (7-4. July 4. Independence Day. Get it?) Once this happens, return to the main menu.
Once back in the main menu, enter 7-4 using your remote. (This may work best by clicking on the +10 key seven times, then clicking 4. This may also work by just hitting 7, then 4. This will vary by player, so feel free to try things out. Note that some players may not support this type of numerical entry.) This must be done before the ship stops moving; otherwise, you will have to repeat this process from the very beginning.
Once you are successful, you will now be able to access an extensive Easter egg supplement menu. The first option is a sound layer demonstration of the aliens' arrival, with isolated dialogue, effects and music tracks (available in either 5.1 or 2.0). The second option shows one of 12 clips of destruction from the film. The third option shows one of 22 news broadcast clips used in the film.
However, within this menu, there are additional Easter eggs. The first egg-within-an-egg can be found by highlighting "Sonic Separator" and pressing right. Press enter to view the disc's DVD credits.
The second egg-within-an-egg can be accessed by typing in 7-2 from the main Easter egg menu. This will allow you to directly access any of the 12 destruction clips from a menu.
The third egg-within-an-egg can be accessed by typing in 7-3 from the main Easter egg menu. This will allow you to directly access any of the 22 news broadcasts from a menu.