She was taken to nearby BIMC Hospital, where she had a part of her skull removed, fluid drained out and a clot removed from her brain.
The bubbly teacher had been in Bali for about a year, teaching English over Skype. She was due to come home on December 14, with plans to continue the job from New Zealand.
But now the family faces a hard Christmas without her, her father said.
"A lot of people say she lights up the room when she walks in. She's a bit different - flamboyant - which is probably why she's over there. She went for a holiday and liked the place."
Hearing their daughter had been in an accident and was on life support was "a heck of a shock to us", Ian said. His wife, Ann, is doing "about as good as me. We've probably lost about 2kg in a week. But we're doing all we can do."
Teenica's condition has improved over the week, Ian said. "She's breathing on her own now. Although she's not talking or doing much yet, the doctors over there seem to think she will come back."
Teenica had taken out insurance solely for the day of her flight in case Mt Agung erupted again, but she wasn't covered for December 10 and her hospital bills are soaring.
Ian, 71, and Ann, 68, have spent about $90,000 at the hospital, including $40,000 for the brain operation. It costs around $3000 per day to keep Teenica in the hospital.
They have contacted the Auckland Air Ambulance who are looking at flying her out on a commercial airline on December 27. That will cost another $72,000.
"I can see it getting up to $200,000 at the finish," Ian said. "It's coming out of the money we had saved for our retirement.
"But you can't put a price on life. We've got to get her out of there, that's all there is to it."
Teenica's sister, Patrice, and son, Jason, are in Bali at her bedside but will fly back on December 21.
"Her injuries are substantial and we would appreciate any help towards getting her well enought to come home to her loving family," wrote Trevor and Sharryn Harrex on GoFundMe.
"Teenica's parents are heart broken to say the least and it is Christmas time as well so even harder," they wrote.
"This is our way of helping to get Teenica back home to her family and we would be so truly grateful if you can help in anyway."