Ms Still and her boyfriend Chrisjan Jordaan jumped from the balloon basket when it was still entangled in the wires. They died from their injuries.
The other nine people, including Mr Hopping, remained on the burning balloon until it crashed to the ground.
Today, Mr and Mrs Still told the inquest their evidence provided a voice for their daughter, and sought to make sure no other families would ever endure the pain at losing a child in an avoidable accident.
"She was an open person and gave herself freely to others," Mrs Still said of her daughter.
"She was a leader, she was a funny person, she would light up the room with her presence."
"Had she not died prematurely in January 2012, she would have continued to make a difference in the world," Mrs Still said.
Her daughter and Mr Jordaan were "so in love" with one another, and the balloon trip was a gift from Chrisjan to Alexis, Mrs Still said.
Mr Still told the inquest his daughter had reassured him on several occasions Mr Hopping was the "safest" pilot in New Zealand.
She would not have boarded the flight if she had known he did not have a current medical certificate, he said.
Mr Still also asked Coroner Peter Ryan for a raft of recommendations addressing problems with the accident, including the enforcement of random drug and alcohol testing in the adventure aviation tourism industry.
Toxicology results showed Mr Hopping had cannabis in his system at the time of the accident, and impairment of the drug could not be ruled as contributing to his judgement in his errors.
He also asked for a review into the process of identification following crashes like the Carterton balloon accident, after his family were made to wait four days to see the body of their daughter - even though she had not been burnt by the fire.
The inquest, at Wellington District Court, continues.