Nice man! As a CMDR who always flies solo, this is not at all unreasonable to accomplish and will improve your skills greatly. You can even succeed in these missions with small ships, trust me. The key to these encounters is patience and being able to kite well along with being able to eliminate targets efficiently. Speed and efficiency in bringing each individual conflict from initial shot to pop is crucial, and your build should be to suit this principle alone. Time is of the essence. It's best to deal with ships in order of their speed, fastest to slowest. The slow guys you can effectively ignore as you pick off the faster guys while kiting the mob of slower guys to effectively neutralize their offense. Once the fast guys are taken care of, you can get to work on the slow guys who can't keep ToT. Assuming you are using a fast, nimble ship and fly competently, it's just a matter of time.
o7