Step 1: Pick a mammal. It helps if the beast is in any way ferocious or unpleasant to begin with, but this is not necessary because of....
Step 2: Science can be whatever you want it to be! Don't worry about taking massive leaps of logic or using the phrase "genetic engineering" as a simple, two-word explanation for how your mammal can fly/think/shrink/grow/turn invisible/pee acid. Your audience probably has an average age of 15; they have no idea how gene splicing or nucleotide sequence mutations work, so why should you?
Step 3: Take your time. Giving the monster screen time is expensive, and gives the audience time to scrutinize your makeup effects. Jaws and Alien proved that the less you see of the monster, the more terrifying it is; your movie is just as good as those, right?
Step 4: Your characters will probably have to be scientists in order to cram them into your storyline. Not to worry; scientists, when confronted with Killer Mutant Mammals, will panic, lose their faculties, and be able to do all the stupid things that we have come to expect from 17-year-old girls being chased by undead serial killers.
Step 5: Rock the Split Diopter:
If you can't afford to rent a split diopter, there are many other ways to add a bit of pretentiousness to your Killer Mutant Mammal Movie. Try over color-correcting until there is nothing left but blues and grays, or using lots of dutch angles. Your imagination is the only limit -- not logic, coherency, taste, or anything like that.
The Boxer's Omen (Chin Hung Kuei, 1983)
12 hours ago