I would imagine you’re talking about plexiglas (perspex in the UK),
also commonly called acrylic glass or just acrylic, the scientific
name of which is poly (methyl methacrylate).
There is a related polymer, poly (methyl acrylate) which is softer
due to the fact that the polymer backbone does not contain the extra
methyl (CH3) group that poly (methyl methacrylate) contains. So the
chains can slide against each other more easily, making it softer.
I’m not sure which one is used in hydraulic forming, but a website I
looked at, advertising a hydraulic forming workshop given by Dominic
Lowes and Tony Eccles talks about the use of acrylic “puffing” dies,
so it suggests plexiglas.
I’m sure someone who actually knows about hydraulic forming will be
able to clarify it.