The Predation of the Moa shaped the evolutionary history and eventual extinction of these giant birds. For thousands of years, the main natural predator was the Haast's Eagle, which evolved massive size and strength to take down even the largest moa species. With talons as large as a tiger’s claws, this eagle could kill birds that were several times its own body weight - teara.govt.nz 
In addition to the Haast's Eagle, moa chicks and eggs were vulnerable to smaller predators. Native Eyles's Harrier and the New Zealand Falcon may have preyed on young moa, while ground-dwelling birds such as the Laughing Owl could have exploited eggs or fledglings.
However, because New Zealand lacked mammalian carnivores before human arrival, these pressures were limited and did not threaten moa populations overall - britannica.com
The greatest predation pressure came with the arrival of the Māori around the late 13th century. Skilled hunters, they rapidly exploited moa as a food source, targeting both adults and eggs.
Unlike avian predators, human hunting was systematic and combined with habitat burning, leading to the extinction of all moa species within little more than a century. This sudden collapse also drove the extinction of the Haast's Eagle, which relied on the moa as its primary prey - nzgeo.com