I suggest this copolymer: Poly(dl-lactide-co-glycolide).
I am sure that this copolymer is biodegradable from an unpublished M.Sc. thesis. As for the tensile strength, please consult relevant literature because I do not have references, unfortunately.
@Ricardo, surely your questions brings in some purpose.
High in this case is an imaginary variable. A variable powerful enough to resist deformation or rupture when you apply a decent force perpendicular to the film with your mighty thumb.
That sounds to me like an application for PLA film. Look for it by name many suppliers: nature works, toray and many others. It will hydrolyze with water. Not too sure about its biodegradability