Went to Argentina 5 years ago to hunt for Asian Water Buffalo and doves. Took along my Ruger Hawkeye African .375 Ruger and a Browning semiauto 12 ga. Getting the guns into the country was not difficult, but the pre-travel paperwork required a lot of data on the firearms, including barrel length, etc. in order to get the necessary permits.
Flew into BA, and at customs was immediately hit up for $160 cash, in order to proceed.
Once at hunting camp, about a 10 hour drive from the airport, wife and I enjoyed incredible food and accomodations. First up was the hunt for a buffalo bull. After finding and stalking several different bulls, I finally connected with one on day 3. After the buff hunt, it was off to the dove fields, for three days of crazy shooting for doves, and parakeets, which are a real pest in farmlands. I shot so many rounds of ammo at doves etc. that I finally just got tired of shooting!
Would love to go back, but next time just for doves and waterfowl. I would use camp shotguns and forego the whole firearms airline travel drama entirely.