"They want to make sure this never happens again in another circus act," said Michael Krzak, an attorney for seven of the eight women, told reporters in a press conference on Tuesday.
The acrobats were part of a hair-hanging stunt during a May 4 performance at Ringling Brothers and Barnum and Bailey Circus' Legends show. The stunt, described as a "Human Chandelier," required them to hang in the air by their hair.
But the carabiner snapped, according to a later investigation, causing them to drop 40 feet to the ground.
"My dream was to be a star performer," Julissa Segrera, 20, said. "Now my dream is to get up and walk."
Lawyers said they are still figuring out which parties to sue pending a complete investigation of the accident.
"We and everyone at Ringling Bros. definitely as a whole, continue to wish them a speedy recovery," a rep for Feld Entertainment, which owns the Ringling Bros., said in a statement. "And we would welcome them back to the Greatest Show on Earth with open arms" if they choose to return.