However, Georgia did not give up and kept punching the crocodile with all her might.
The guide - apparently a German national who was not registered with the tourism authority and has since fled - insisted it was safe to swim.
She said she was proud of her "feisty" sister Georgia, who has now been released from hospital after being treated for the injuries she got while saving Melissa.
"Georgia punched the crocodile repeatedly as it came back three times to attack, while friends of theirs went to get help", she wrote in a Facebook post.
Georgia added, in a WhatsApp voice message to her family: 'She's been breathing on her own very well.
"She's had a couple of operations on her wrist and her abdomen, so we are hoping that she will just have a little more time to have restorative rest in the medically induced coma but we're hoping that in the next couple of days we'll be able to see some improvement on that". Notably, she had heard that with some animals, one has to start hitting them to scare them away, especially when they are hunting.
Speaking about Georgia's heroics, she said: "She was very courageous".
Melissa's condition remains "delicate" but they've now been linked with a "fantastic" doctor who's helping the family communicate with the hospital she's at, Hana added.
A GoFundMe page set up by Hana to raise money to help cover medical costs for the twins has raised almost £38,000.
But their older sister says Melissa's situation is "still really serious" and "we're not relaxing just yet".
Writing on the page, Hana said: "Georgia has been discharged from the hospital and remains nearby to continue with dressing changes and treatment etc".
But Melissa must overcome her physical injuries and both women will need time to deal with the emotional and mental fallout of what they have been through.
Georgia also suffered extensive bite wounds to her arms and hands.
"There's now no change in information for Melissa's condition which remains "delicate", but we think stable".
But following the ordeal, their parents are now considering flying out to Mexico to bring them home.
Georgia fought off the crocodile to save Melissa's life.
They had been travelling, volunteering and working in animal sanctuaries, their sister Hana told BBC Radio 1 Newsbeat.
However, when Georgia realised that the reptile was trying to drag her sister underwater, she overcame her fears and punched it in the face. "She kept punching it in the head".