SNH has launched a five-year pilot project to protect ground-nesting birds including curlews from predators.
But the scheme, which involves issuing licenses for a cull of ravens at Strathbraan in Perthshire, has sparked public outcry and conservation groups have hit back.
Springwatch presenter Chris Packham has written an open letter to SNH chairman Mike Cantlay warning the plan will "incinerate the last vestiges of credibility" of the public body.
And the petition claims the project gives license to "every raptor and corvid persecutor to take out their guns in what could be a mass slaughter". Campaigners behind the petition are only 800 signatures short of their 35,000 supporter target.
In Mr Packham's statement, which was posted on Twitter, the conservationist said: "If you had asked a term of the very best PR executives to come up with a plan to incinerate the last vestiges of credibility, to banish any dwindling reserves of integrity and to destroy any remaining trust between conservationists and SNH, then it's my bet that they would have suggested this.
"As it stands the already beleaguered reputation of SNH lies in bloodied tatters and, whilst I am not a PR person, I would suggest that to reverse this ill-judged and ruinous decision as quickly as possible would be a good idea."
Commenting on the online petition, one supporter described the policy as "unethical" and "counter-intuitive" for a natural heritage body. Another backer simply branded the scheme "sickening behaviour".
During the consultation process for the controversial pilot scheme RSPB Scotland expressed concerns. A spokesman warned general licenses wouldallow "unrestricted and un-monitored killing of otherwise protected species".
General licenses are issued regularly to allow land managers to kill protected species including gulls, magpies and crows when they are damaging crops and livestock. The RSPB said the license system can be used as 'cover' for criminal destruction of birds, particularly with cage traps.
Ian Thomson, RSPB Scotland's head of investigations, said his organisation recognised that legal control of some bird species such as crows can has conservation benefits for wading birds, red grouse and some other ground nesting birds but added that SNH's plan extended an already risky system.
In a statement, SNH said the scheme was prompted by the "comprehensive" Understanding Predation report of 2016. The spokesman said: "The limited trial at Strathbraan in Perthshire will explore whether the reduction in ravens will help curlew and other ground nesting birds to recover.
"The habitat here is good for breeding waders but raven numbers are increasing."
SNH has already rejected claims from some campaigners, including Raptor Persecution UK, that the trial will open the door to the illegal killing of birds of prey.
The heritage body added: "We deplore the illegal killing of birds of prey. Where we find evidence of crime, we support the police to secure convictions."
The Countryside Alliance has thrown its support behind SNH, praising them for prioritising "science over emotion".
Jamie Stewart, Scottish Countryside Alliance director, said: “Culling any species is controversial, but the conservation of our beleaguered waders is too important an issue to be decided by emotive campaigning. Any approach needs to be grounded in science, and that’s why we welcome this research licence."