Conway, Newton and Alcala bring back Hugo Strange to face Batman directly for the first time in eight years in Batman 356 (Feb. 83).
The last time he had dealt with Batman he had learned that the hero was Bruce Wayne, and had also taken to wearing the Batman costume himself. Both of those facts are central to this story.
Despite his feelings of responsibility for Catwoman, Bruce Wayne is also carrying on with his romance with Vicki Vale, the cad.
When Vicki gets a call from the paper, she has to take off, but arranges to meet Bruce later at the Manor. Bruce drives home, and think he must have daydreamed, as he gets there much sooner than expected. But once in the house, Alfred promptly tries to kill him. He fights the deranged butler off, killing him, only to have the body vanish, and Alfred show up all normal.
The reader quickly gets cued in that Bruce is not really at home, as we see Vicki arrive, running into Alfred and Dick, all of whom are puzzled that Bruce has not come home.
Meanwhile, Bruce gets attacked by Robin, and the scene plays out much the same way, as he kills the boy, who disappears and then returns as if nothing had happened.
Heading down into the Batcave, Bruce finds Hugo Strange, having shaved off his beard and adopted the Batman costume. The people Bruce had been fighting were all robots, as Strange was toying with the hero. But now it’s time for them to go at it one on one, to determine which of them will get to be the Batman.
Strange also fills Batman in on how he survived his apparent death at the hands of Boss Thorne, and how he then spent all those many months taunting and tormenting the mob boss. Strange is clearly a much better fighter than he would appear, as he and Batman fight almost to a standstill.
But Robin shows up, having gone looking for Bruce, and together they defeat Hugo Strange. But not one to be taken in, Strange then blows up his fake Wayne Manor, once again apparently dying in the blast.
But Hugo Strange is never really dead, and will return three years down the road, just before the end of the pre-Crisis Batman adventures.