The secretive organisation is being investigated in several countries over strikes on Visa, PayPal and others.
Over the weekend Aaron Barr, head of HBGary Federal, said he had discovered the names of its most senior figures.
The group retaliated overnight by breaking into the company's website and hijacking his Twitter account.
Anonymous, known for being a loosely-knit group, has been involved in a number of high profile online protests and attacks in recent months.
In December, the group launched a campaign in support of Wikileaks that disrupted services at MasterCard, Visa and other companies that had withdrawn support the whistle-blowing website.
The strike led to police investigations around the world, and a number of arrests in Britain and the Netherlands.
Although the individuals who make up the collective claim they do not have a traditional hierarchy, Mr Barr told the Financial Times that he had infiltrated the organisation and uncovered the names and addresses of several senior figures.
He said he did not intend to hand the information over to the authorities unless forced to, but did plan to present his findings at a conference in San Francisco later this month.
The attacks began shortly after his claims were made public, with a sustained attack that targeted him both personally and professionally.
Mr Barr's Twitter account was filled with a sequence of racial and sexual slurs, along with a string of personal details such as his mobile phone and social security numbers.
Meanwhile, a message on the company's website said that Anonymous had "seized" HBGary's operation in order to defend itself.
"You brought this upon yourself," the statement said.
"Let us teach you a lesson you'll never forget: don't mess with Anonymous."
The group said it had gained control of all the company's e-mail, erased its files, taken down their phone systems and placed copies of many internal documents online.
Mr Barr could not be contacted for comment, but the hacked site was later replaced with a placeholder page.
Anonymous, which started as an offshoot of the notorious 4Chan internet messageboard, has been linked to a number of virtual and real-world protests over recent years.
As well as the Wikileaks attacks, it also orchestrated strikes on government services in Tunisia and Egypt in support of popular protests in those countries.
It has also launched vociferous protests for the right to uncensored access to pornography online and taken action against an anti-piracy firm hired by Bollywood studios.
It is involved in a long-running battle with the Church of Scientology, amid claims that the religious group stifles dissent.
The loosely-organised group has previously claimed it has no real leadership, although some individuals have come forward from time to time to explain their motives.
One, known as Coldblood, told the BBC in December that "thousands" of people had joined the protests to support Wikileaks' right to publish the US government's classified diplomatic cables.
"We are trying to keep the internet open and free but in recent years governments have been trying to limit the freedom we have on the internet," he said at the time.
Coldblood confirmed to the BBC that he was among five people arrested across the UK last month as part of the police investigation into the Wikileaks protests.
tl;dr: Anon has successfully DDoS'd a security firm and what I assume is a high ranking employee has his twitter account wrecked. He had claimed to have the names of leadership within the group. They posted a warning to not mess with them, etc etc, and claimed to have wrecked some havoc throughout the company (probably BSing again).
Opinion: This is pretty over the line, even for anon, and there might be another bout of arrests going on soon. Wouldn't be a surprise, anyway. I really hope they tone down the lashing out for a while.