The popular EM shielding material for about the past 40 decades, for applications requiring the maximum shielding effectiveness, is a material call mu-Metal. (mu = the greek letter µ is the symbol fairly universally used for magnetic permeability).
A minor difficulty is that for best properties it needs to be fully annealed after any cutting and forming, and for best results the annealing requires a hydrogen furnace with both controlled heating and cooling rates. Locating a processor capable of the needed precision sheetmetal handling and processing may be somewhat difficult, unless you have very good contacts within the electromagnetic manufacturing industry.
While almost anyone can make a suitable "tin-foil hat," your truly effective mu-Metal hat may require significant effort and expense, so you should be quite sure of the fit before the seams are closed and final processing is done.
Also be aware that "accidents" that deform the hat may reduce the permeability somewhat below optimum, although with reasonable care in handling the wear and tear of daily use should not have more than minor effect on the protection achieved. As the material is quite dense, and thin parts are sufficient for the EM protection required, separate protection using other materials of lesser density would be preferable if "impact resistance" is also required (to withstand blunt force trauma in the event of something like an alien capture).
Due to limitations on the sheet sizes available, it would be a good idea to order at least two full sheets of mu-Metal for any application such as "full body shielding" if you can negotiate a price reduction based on quantity ordering.
There are other materials claiming "nearly the same" performance as mu-Metal, but the detailed specifications for all of the ones I've found are somewhat inferior, although some of the alternates may offer fabrication process advantages permitting performance similar to what one might get with mu-Metal poorly processed, at a lower fabrication cost.
A possible alternate material might be Giron. Material purchase cost probably is similar to the preferred mu-Metal, but less post-forming processing may be required, which could result in less total cost for your hat.