That is really fast deterioration. Battery may be leaking.
I once fit a metal tray with 'Ice & Water' roofing membrane. Actually worked quite well! Very cheap, since I had a big roll anyways. A roll of the 6inch wide stuff for sealing around windows is only about $12 at the home center.
Performance Products and some other places sell special battery tray liners that neutralize acids.
I have seen cars refit with marine-type battery boxes as well, but could be a tough fit for many cars.
Some folks swear by spiral-cell batteries like Optima. These can be mounted upside down without leaking.
This place has mats too: