The big cover is attached to the engine via four plastic posts that sit in rubber grommets. If the cover was assembled dry, the plastic doesn't want to let go of the rubber, and you'll just pull and pull and pull.

I took a can of WD40, and while lifting the front passenger side of the cover (you might need a helper for that), flooded the top of the rubber grommet. Eventually it pulled free of the metal bracket which holds it, and the rest came out.

Put a little grease on the top and bottom of the grommets before reinstalling the cover, and the job will be easier next time.

 

Thanks to jdias and Bill6211789, both answers were exactly the information I needed to do the job. I was able to remove the cover after you told me what was holding it. What an ordeal. With my GMC and Ford Pickups it is just two screws or snaps and there the filter is. I can change those in 5 minutes. This Passat took my at least 45 minutes. A dozen screws, two air flow vents, an electrical plug-in and then when putting it back together you have to position the filter so that you can put it back together. Whew. But I sprayed the posts and fittings with white grease. Should be a lot easier next time.

 

http://www.swankmonkey.com/vw/jetta/2006/remove_engine_cover/

-pull up and towards the front of the car. Try doing while the car is hot also it makes the rubber gromtes slightly softer
x2 about the grease so the next time you try it's not so much of a PITA

-then after you have the cover off this is how to change the filter

http://forums.vwvortex.com/showthread.php?2547554-Howto-Change-FSI-(2.0T)-Air-Filter-PICS