I swear this unit was designed not to be taken apart, despite the manual blithely stating you may need to change the battery one day. There are at least 3 clip elements to each half of the cover, and they require moving in opposite directions. The key one seems to be at the top of the font, where the round nodule sticks out. The top part of the cover is clipped behind the lower. Push the lower part back and up while pushing the upper part down and out. With any luck you'll free the two enough to skew one side of the upper cover off entirely. That's when all the innards drop out!
You may need this schematic to put it back together again - I did.
http://www.shouldersofshoreham.co.uk/sos_17Bamp.mvc?c=9648545
Good luck!
David Price
May 2008