Zampa said despite enjoying an upperhand over the Indian captain in limited-overs, Kohli is a hard nut to crack.
"It's going to be an attacking approach. I think if you're on the back-foot and have a defensive mindset then that's when he (Kohli) can get on top of you. The most important thing playing in places like India against these guys is to have a little bit of character," said Zampa ahead of Friday's second ODI here.
Zampa has dismissed Kohli four times in ODIs and twice in T20s.
In the lung-opener in Mumbai on Tuesday, which Australia won by 10 wickets, it was Zampa who took a sharp catch of his own bowling to dismiss Kohli.
"You probably know you're going to get hit for boundaries but it can really get worse if you make that affect you. I have got him a few times now but I don't think there is anything in it. He still scores at over 100 (strike rate) against me," the 27-year-old spinner said.
"He is a very hard guy to bowl to. He's one of the toughest guys I've ever had to bowl to. After game one (first ODI), he will be even more switched on. It will be a big challenge," said Zampa, who has 66 ODIs wickets from 49 games.
Kohli had recently showered praise on Zampa, saying in Australia's last tour, the leg-spinner had more belief than other bowlers.
Asked Zampa about Kohli's comments, he said: "It's a big compliment from Virat. I'm not the most skillful leg-spinner in the world. Guys like Kuldeep Yadav and Rashid Khan are guys that are really hard to pick. But one thing I have always tried to do is have a strong character."
Steve Waugh had said in the past that Kohli has not shown enough respect to Zampa, but the leggie disagreed with the former Australia skipper.
"I don't think he (Kohli) doesn't respect me. I don't think that's correct (referring to Waugh's statement)."
Zampa said Australia has managed to find out Kohli's weak point.
"We basically just found that Virat finds leg-spinners hard to line up early in his innings. He's such a great starter, even the other day he was 16 off 14. How much energy he brought to the crease, his running between the wickets, some of the cover drives he played off the quicks," he said.
"I think it's important to try and have a game plan against him. So we figured out before the last game that it would be good to start with leg-spin to him.
"I've got him out four times in the last year or so it's nice to have that confidence to bowl to him at the start of his innings," said Zampa, who is on his third tour to India.
For record, Kohli has been dismissed 55 times by spinners in his ODI career so far.
Zampa said it is not easy to be a wrist spinner in ODI cricket.
"To be a wrist spinner in one-day cricket in the middle overs is not easy at all. It's probably one of the hardest formats," he said.
"At least in T20 cricket you have five guys out the whole time and you know that guys are going to attack you. That's fine. But one-day cricket is a whole different beast."
Australia is on the cusp of registering back-to-back series win in India, a rare feat for any touring side.
"We played really well in those three ODIs in February (last year). It's going to be a big deal if we can get two away series wins in a row in India, so we have spoken about that briefly," Zampa signed off.