The instructions with mine seem pretty clear that this is NOT a user option.
I don't know if a Scubapro/Uwatec dealer can do it (in which case it
certainly could be a user oprion) of it has to go back to manufacture.
In either case, a dealer should be able to take care of this.

Uwatec Aladin computers are sealed in the same way as the digital depth
gauge.  Aladin computers are liquid filled.  I would think that Uwatec
probably used the same technique in the manufacture of the depth gauge.  If
so, it is not probable that you would be able to open it, change the
battery, fill it with oil again and seal it so that it would work again.
Why not just have your local Scubapro shop sent it back for a battery
change.  If Scubapro will replace the battery they will recalibrate it as
part of the service.  If they won't replace it, buy a new one - they aren't
that expensive and you have probably gotten your use out of the old one by
now anyway.  I have three or four of them.  I am pretty sure the oldest of
them is about 8 years old and they are all still working.

Safe diving,
Cpt. Dale

Computer?  There are two ways, the hard way and the expensive way.
The hard way can also be expensive if done wrong.

You will need to get a special tool to open the battery compartment.
I think angled needle nose pliers will work.  You remove the battery,
unsolder it and solder the new one in place.  Then you replace the
cover.  Afterwords, you hope the cover is secure and the O ring is in
good shape.

The expensive way is to send it back to Uwatec.  Find a LDS that
services Uwatec and they will be more than happy to do it for you.