The bonus disc for each film contains a hidden DVD credits section. The access process for each is the same: To access these, click on "Navigation Options" from the main menu. Once in, type in the theatrical release corresponding to the film covered on the bonus disc. Here are each film's release date for easy reference:
Alien - 5/25/79
Aliens - 7/18/86
Alien3 - 5/22/92
Alien Resurrection - 11/26/97
Like many other Easter Eggs involving numerical entry, there may be many different ways to enter and access this egg. For example, one way to make this work is to type in the month & press enter, type in the day & press enter, and type in the year & press enter. (I was also able to get it to work by just typing in the month and year - no day was necessary.)
In addition, there are two more significant Easter Eggs: video pieces featuring some of today's top DVD producers and their involvement in the Alien saga. The first is found on the "Aliens" bonus disc. From the main menu, click on "Post-Production". Once in, highlight "The Final Countdown" and press up. Hit enter to watch Van Ling discuss a "power loader" costume he built and the beginning of his career with James Cameron.
The other video piece is on the "Alien Resurrection" bonus disc. From the main menu, click on "Post-Production". Once in, click on "More" to go to the second page. Highlight "Back" and press down. Hit enter to watch David Prior discuss his acting experience as an alien in the film.