Lynne Owens, the agency's new director general, said her priority was to "relentlessly pursue" the "kingpins" of organised crime gangs.
A list of up to 100 leading gangsters was being compiled by regional police units, she said in her first speech since taking up the post.
These criminals were involved in drugs, guns and human trafficking, she said.
Until now the agency, known as the NCA, had spent a lot of time combating the "tier below" the top criminals, she said.
Local forces and regional crime units had now advised that they were capable of pursuing lower tier criminals - leaving the NCA to tackle top targets.
"Our focus will be on the so-called untouchables, those who have sought to build industries of organised crime," she said.
"We will ensure that none of them are beyond our reach, no matter how sophisticated their offending: put simply, there will be no hiding places."
Some of the "untouchables" spent time abroad or moved money overseas, she said.
They were motivated by money and controlled groups involved in drugs trafficking, child sexual exploitation, human trafficking and firearms importation, she added.
"These are criminals who terrorise communities and believe themselves to be untouchable," she said.
"They create a misplaced sense of power, status and position, often abusing vulnerable people to undertake criminal activity on their behalf, distancing themselves whilst taking most of the profit but none of the risks.
"They can become negative role models to some young people in the process."
Such criminals should "fear" authorities' access to intelligence, skilled and determined staff and unassailable evidence presented in the courts, she said.
Asked what was different about the NCA's pledge to crack down on "untouchable" criminals, and other similar promises by senior police officers and politicians, Mrs Owens pointed to the "very good" working relationships with domestic and overseas agencies, and new capabilities at the "top end".
"We now have the tools available to us," she said.
The "untouchables" of the UK's criminal underworld will have no "hiding place", the National Crime Agency's chief says.