1. It was legal.
First off, Bachman was doing something completely legal with a permit, not to mention paid thousands and thousands of dollars to hunt legally inside South Africa. The anti-hunting lynch mob has implied she did something illegal. She didn't.
2. It was not "pure sport"
The petition and description from Change.org are dishonest. Bachman wasn't hunting for "pure sport." All of the meat from the lion was donated to people in need, which is standard practice for a majority of Africa hunts.
Hunting lions keeps the population in check so lions don't overeat prey, other lions or starve to death. It would be nice if anti-hunters did their research about how anti-hunting policies negatively effect animal populations of all kinds. If they did, they would know hunting bans only result in tainted gene pools and starvation. It's called sustainability.