Mildew is a common name for a variety of molds, which are ubiquitous in our environment. If mold has damaged a pair of boots, there is nothing you can do to eliminate the existing damage, but you can stop additional damage from happening.
First, put the boots on a table and using a slightly damp sponge, gently rub off as much exposed mildew that you can see. Clean the sponge regularly, as you don't want to spread around mold spores. (Wear gloves on your hands and consider a dust mask to protect yourself, too.) Do NOT use soap or detergent. Just water. (When you're done, wash your hands thoroughly with soap and warm water.)
Second, get Lysol or Clorox disinfectant wipes – they come in a canister and you can find them at a well-stocked grocery or drug store. The active ingredient in these wipes working for you is a disinfectant whose chemical name is Alkyl Dimethyl Benzyl Ammonium Chloride. N.B.: the active ingredient is not sodium hypochlorite (chlorine bleach). This chemical kills mold that is growing, but does not kill mold spores. That's why you should use many of the wipes when cleaning leather, so you don't spread the microscopic mold spores to other areas of the boots (and another reason to wear a mask, so you don't inhale the spores which can cause a nasty infection). Rub the wipes not only the directly-affected areas, but all over the boots, since it is likely that spores are on them in places that you can't see.
While these wipes are convenient, an alternative is to dilute one cup (236ml) of denatured alcohol (not isopropyl or “rubbing” alcohol) to one cup of water, and paper towels. Dampen a paper towel in the solution, wring it out, and then use it as a wipe. Do not re-use a paper towel wipe, even though it may not look like anything is on it. Spores are there; you just can't see them. Alcohol kills growing mold, but also can dry out leather easily, so don't soak the leather in the alcohol solution.
Do not use any form of bleach or Lysol spray directly on leather boots. You'll ruin them.
Third, replace the natural oils in the leather by conditioning the boots. Use Lexol leather conditioner (or similar product) and following the directions on the container, gently treat the leather on the boots. Use a little bit and treat small areas, overlapping. Take your time. The more time you spend in applying conditioner slowly and evenly, the more likely the damage will be minimized and perhaps reduced to being unnoticeable.
Avoid the urge to polish the boots after applying conditioner. Let the boots dry thoroughly and allow the conditioner to soak deeply into the leather.
Place the boots in a cool, dry place, out of direct sunlight. Keep them away from air blowing from a duct, such as AC or heat. But if air doesn't naturally move in the room where you have the boots, put a small fan on the floor to circulate air in the room.
Let them dry for a day or two, and check them. You may need to use the wipes to clean off any more mold that might have regrown or that you missed before, and recondition any area on which you have used a disinfectant wipe.
Once the mold and mildew are removed and the boots appear clean, you should polish them.