This is the name of the Co.

I would like you to consider that this IS a name and names are not ususally translated.
Food for thought...

perhaps a developer of medical items?

It is possible that this is an institute of training, as an academy often is. However, it is more likely that this association is a learned society. The word Bildung does not refer to career-oriented training. It is the kind of training people mean when they speak of well-educated persons. General polish and knowledge are meant. Gesellschaft is a society, not only a business. So it is in my opinion more like the "Royal Academy". Either way, the above translation works.
While names often are not translated, I do translate the German names in my resume. Technische Hochschule gives the wrong impression, or none at all.

In the translation of certificate itself I would go with Dierk and just repeat the German legal name.
According to the scant Web information, the Zittauer Bildungsgesellschaft gGmbH supports both medical (Krankenpflege) and technical/engineering programs. There is no context to suggest which program the certificate holder has attended. This should of course be clarified in a covering letter, in which the legal name could be followed by a translation, e.g., Zittauer Bildungsgesellschaft GmbH (Zittau Educational Association).
The only school listed in the official register of schools in Zittau is the Medizinische Berufsfachschule (Krankenpflegeschule) der Zittauer Bildungsgesellschaft gGmbH.
http://www-db.sn.schule.de/scripts/schulen/gemeinde_execg.as...
http://www-db.sn.schule.de/scripts/schulen/eintrag.asp?Id=31...
But another Web page supports a technical engineering direction, perhaps in a separate activity supported by the same association.
http://www.zittau.de/vhs/Schwerpunkte.html