Ulsan finished sixth during the regular season, but overcame FC Seoul, Suwon Samsung Bluewings and Pohang Steelers to book their place in the two-legged championship decider, with the first game taking place on Wednesday.
And despite the number of scalps his side have claimed along the way, Kim knows Jeonbuk will pose their biggest test yet, especially with the experienced Choi Kang-hee at the helm.
"Choi Kang-hee is different. The managers of Seoul, Suwon and Pohang are all young and inexperienced," Kim said.
"Choi has a lot of know-how. So it will be a difficult match.
"We are the underdogs. We have qualified for the finals despite finishing in sixth place during the league. But we have had a good run and are full of confidence."
Meanwhile, Choi is hoping the final will provide his charges a chance to redeem themselves following their AFC Champions League defeat at the hands of Al Sadd.
"We are now one of the giants in the K-League," Choi said. "This will be the opportunity to cement our club status in the league.
"We can become a notable club by winning the final. So it is very important to get a proper result."
Ulsan last won the K-League in 2005, while Jeonbuk's previous triumph came just two seasons ago.