Godzilla nearly killed King Ghidorah in their second encounter in Godzilla: King of the Monsters, but Godzilla needed help from Mothra to win the final battle. Godzilla and Ghidorah battled at three different points in the movie, with varying results. The first fight had no clear winner, but it did appear that Godzilla was gaining the upper hand. Their second battle, however, was much more conclusive. Godzilla ripped off one of Ghidorah's heads, and likely would have finished the job if he wasn't hit with the Oxygen Destroyer.
Their third and final showdown unfolded quite differently. Though both were getting in their fair share of blows, Godzilla seemed to be winning, but soon the tide turned in Ghidorah's favor. Despite being powered up by the radiation he had soaked up in the underwater civilization, it didn't seem to be enough to beat Ghidorah, who was hitting him with everything he had. After being dropped from the sky, it looked as if victory was assured for Ghidorah. But after Mothra used her life force to refuel Godzilla, Godzilla entered his burning form and easily eviscerated Ghidorah with his atomic pulses.
Does the fact that Godzilla would have lost without Mothra's help mean that he isn't the true King of the Monsters? No, because there's a good reason why Godzilla suddenly couldn't beat Ghidorah alone. Ghidorah has an ability to absorb energy. The novelization reveals that when Ghidorah stood on the volcano and regenerated his missing head, he was actually drawing energy from the volcano itself. If he retained any of this energy following the regeneration, his power would be at an increased level. So Godzilla needed to be powered up as well in order to defeat the three-headed monster.
Later in the movie, Ghidorah bit into a power substation and drained the energy from it during the final battle. This provided him with a massive boost of power that seemed to trump Godzilla's own upgrade. Ghidorah's energy absorption ability wasn't a factor during their earlier battle. King of the Monsters director Mike Dougherty has confirmed that Godzilla would have killed Ghidorah if the humans hadn't interfered.
While it could be argued that Ghidorah, not being able to fly away while in the ocean, was at a disadvantage simply because he was in Godzilla's element, there's another way to prove that Godzilla is superior to Ghidorah in combat. Godzilla and Ghidorah, who are ancient rivals, fought thousands of years ago, with Godzilla emerging as the winner. So when each monster only fights with their own natural power, Godzilla wins. All things considered, it's clear that despite receiving assistance from Mothra, there's no disputing that the title of "King of the Monsters" always belonged to Godzilla.
