This is my method, and it works great - but bears and pigs are definitely the most challenging:
1. Soak skull in 5gal bucket of water w/several ounces of Rid-X, or any other commercial septic bacterial treatment. Attach aquarium heater to inside of said bucket, and secure a proper position - set temp. to it’s highest setting - generally 90deg F. You may want to build a wire-framed cage to set in the bottom to capture teeth that will most certainly fall out over this long process….
2. Cover bucket with a black garbage bag and secure with bungee cord(s) around the top rim of bucket. You will lose water to heat/evaporation, and will help keep the critters and flies away from this Godawful stew; did I mention to keep this bucket at least 4 city blocks away from your domicile, lest you want to get divorced?! This process is rank…..
3. Change out water every week or 2. Preserve up to 1/4 of previous liquid or supplement w/more septic treatment. Continue this process for at least a month, but for bears & pigs, I’d allow for 2-3 (sometimes longer). The reason I bothered to go thru this long explanation at all is because I’m convinced this temp.-controlled long maceration process is THE best method of removing sinus material, preserving the nasal bone structure AND beginning the degreasing process. You will notice grease/oil floating/collecting at the top of the water bath each time you go to change/supplement….
4. When you feel you’ve macerated long enough, put skull in for a 1st simmer with a scoop of Oxyclean and a couple squirts of Dawn. I never let the the simmer get above 180deg, and never longer than 30min - and I rarely have any problems with the bone sutures falling apart or teeth falling out.
5. Do the simmer process as many times as you feel needed to remove all grease and oil, but I’d be careful with the Oxyclean too many times; it will make the bones brittle/flaky. In fact, I switch to a simmer w/3% hyd. peroxide - just dump a whole bottle into 1 of your simmer sessions. This will purge grease and whiten simultaneously.
6. The rest of the whitening and finishing mounting process I’ll leave out; there’s a couple thousand variations; but my long-winded description here has served me really well in getting all the grease/oils out, and provides a final product that can only be rivaled by beetles (and even better, IMHO).
I think the most important ingredient to this process is time - you have to be patient and diligent if you commit to this process - but it works reaalllyy well. You can achieve somewhat similar results by quick boiling and pressure washing, but it’s not nearly the quality - especially with the particularly greasy critters. Hope this helps.