Crows, Grackles, Sparrows, Starlings, Racoons, Rats, Possums, Squirrels, Rabbits etc.
Depending on the distances most birds can be killed with your Gamo Big Cat with a body-shot. Limit your shots to 60 yards....Crows will need a head-shot at those distances.
Fur bearing animals will need a temple-shot to be sure. Limit those shots to 30 yards. Under 25 yards...a body-shot might do.
Make sure what`s legal to shoot with an airgun in your area/district!
Use 7.5 grain or heavier pellets.....but not over 10 grains (Too light or too heavy a pellet could shorten the life of your spring and other components). DO NOT USE the PBA pellets....they`re way too light.
Very small animals/birds!
But, WHY would you WANT to deliberately KILL, a LIVING CREATURE?
If it's legal to hunt with an air rifle in your state.
The Gamo Big Cat(14.5ft-lbs) is accurate enough and powerful enough to take small game(rabbit, squirrel, etc) and pest birds out to around 35 yards.
You should always use the pellets your rifle prefers(accuracy) but generally speaking domed pellets are the most effective on small game. While wadcutters are on pest birds.
Jim Chapman hunting with his favorite air rifle the .177 caliber Beeman C1(13.3ft-lbs)
Among the small game Jim takes on this hunt is a rabbit at 44 yards. This is not a stunt shot, but an example of what an accurate, medium power air rifle is capable of in the hands of someone skilled in its use.
Real answer. I am an Alaskan certifed hunter safety instructor.
Hunters who have a license can only take the species of animals listed in the regulations when they are in season. Any animals that are not listed in the hunting regulations - nobody can kill.
Every state has laws against animal cruelty. Anyone who harms, injures or kills an animal not listed in the hunting regulations can be arrested and tried in court on animal cruelty charges. This can get you a few days in juvie hall and the rest of the year on probation.
The only exception is vermin like rats and mice. These you can dispatch. The rest you must leave alone.
This assumes its legal to use an airgun to hunt with where you live... It is your responsibility to check the hunting regulations to make sure of this before you go hunting with an airgun.
The Gamo Big Cat produces around 15 ft-lbs of muzzle energy and enough impact energy for most small game (squirrels, cotton-tail rabbit, jack-rabbit), vermin (mice & rats) and nuisance birds (English sparrows, starlings, and feral pigeons). In fact, provided you limit yourself to head-shots, the Big Cat will be limited by accuracy constraints rather than power constraints. If you take body shots, I doubt you'd have much luck with anything bigger than a cotton-tail rabbit. And even then you'll be limited to 25-30 yards at most...
The Gamo Big Cat does NOT produce enough energy for animals like raccoons, oppossum, nutria, fox, etc... These animals are just to large and tough to be sure of a clean kill with one shot from a Gamo Big Cat.
Time, your chances of ever having a girl friend, and any respect in the hunting section.
You should read your state's hunting laws. In that you will find the minimum caliber requirements for hunting birds and varmints. You will also find that a hunting license is required after you graduate from a hunter's education course.