The usual way to tie Cheney to Halliburton is to state the obvious fact that Halliburton has made out like a bandit in Iraq, while still making annual payments to Cheney. A more interesting feature of Cheney's experience in Halliburton is his acquisition of a company without doing due diligence, leading to major liabilities for Halliburton.
The same lack of due diligence is shown in the way he helped stovepipe intelligence from Iraqi con man and Iranian agent Ahmed Chalabi. His refusal to do due diligence, which led to over 1000 American deaths, is exactly the same as what he did to Halliburton, and shows an ongoing pattern in which Cheney believes what he wants to believe, and neither looks beneath the surface nor does any alternative scenario planning..
In 1998, when Cheney was Halliburton CEO, he acquired Dresser Industries, a company which later turned out to have major asbestos liabilities- estimated at several billion dollars and well over the purchase price. By the time this was discovered (together with a number of other liabilities he left the company with), of course, Cheney had left the company with a multimillion dollar profit from stock options.
Edwards of course has been hammering on the corruption implicit in handing Halliburton multiple no-bid contracts in Iraq, and obviously he should keep hammering on that. But I think it also makes sense both to point out what a rotten job Cheney actually did out in the business world, and how the same faults he displayed there are showing up now with far greater consequences. At the least, it may be a line of attack that Cheney isn't expecting.