But Senior Constable Paul Topham said they were foiled by the justice system and a flawed police database.
Luke Batty was killed by his father Greg Anderson at a cricket oval in the Melbourne suburb of Tyabb in February. Anderson was shot dead by police.
A probe into how authorities could have stopped the killing began on Monday.
Snr PC Topham said on Thursday that the police "weren't mucking around with [Anderson], we were trying to get him... we were all working hard behind the scenes to try and apprehend this guy".
"We put him up before the courts and the courts let him out. We've gone the mental health route, it didn't work."
'Astounded'
In his account of events since he first arrested Anderson in January 2013, Snr PC Topham painted a picture of Anderson as an intelligent suspect who knew how to stay out of police custody.
Snr PC Topham had arrested Anderson after he assaulted and threatened to kill his former partner Rosie Batty. He said Anderson "became extremely aggressive" at the arrest, but was "smart enough to shut it down before it got to the next level".
A court decided to grant Anderson bail, which "astounded" Snr PC Topham. "We knew it was a marginal address that he'd disappear from after a few days," he said.
Snr PC Topham said Anderson later changed his address and was unable to be tracked down, and also knew a procedural loophole that ensured he did not need to report to the police.
The police issued several warrants to arrest Anderson. Officers had served papers on Anderson two weeks before the killing, but could not arrest him because of a flaw with the police database.
Snr PC Topham said he considered Anderson "100% bad, not mad", adding that he had no regard for authority and "knew what he was doing".
The Luke Batty case has shocked Australia. Ms Batty has since become a high-profile advocate against domestic violence.
The inquest continues.
Victoria police were "working hard" to arrest an "aggressive" abusive father who later beat his young son to death, an inquiry in Australia has heard.