As an expert fictional battle analyst, I have carefully evaluated the matchups between the My Hero Academia (MHA) universe and the various iterations of Godzilla. Here's a detailed breakdown of each round:

Round 1: Legendary Godzilla (Monsterverse) - The MHA universe has a strong advantage in this round. The collective strength, agility, and tactical prowess of the heroes, combined with their excellent teamwork and support systems, should be enough to gradually wear down Legendary Godzilla. The heroes will likely focus on exploiting any weaknesses and using their quirks in creative ways to gain the upper hand. As a result, the MHA universe is the probable victor in this matchup.

Round 2: Heisei Godzilla - This round presents a much greater challenge for the MHA universe. Heisei Godzilla's enhanced regenerative abilities, stronger atomic breath, and potential energy absorption make it a formidable foe. However, the heroes of the MHA universe have proven time and time again that they can adapt and overcome even the most powerful adversaries. By capitalizing on their teamwork, creative quirk usage, and strategic planning, the MHA universe has a fair chance of emerging victorious in this round, although the outcome could go either way.

Round 3: Composite Godzilla - The MHA universe faces its toughest challenge yet with Composite Godzilla, a nigh-unstoppable force boasting the powers and abilities of all Godzilla incarnations. This round is heavily skewed in favor of Composite Godzilla, given its overwhelming power and diverse range of abilities, including the devastating Spiral Ray, Burning Godzilla's intense heat generation, and even flight capabilities. The MHA universe would need to rally every hero, devise extraordinary strategies, and potentially even join forces with their adversaries to stand a chance against this titanic threat. Although the heroes of the MHA universe have demonstrated exceptional resilience and adaptability, Composite Godzilla's sheer power makes it the likely victor in this round.

In conclusion, the MHA universe fares well against the less powerful versions of Godzilla, but faces increasingly difficult odds as Godzilla's power escalates. The outcomes of the battles hinge on the heroes' ability to effectively utilize their quirks, exploit Godzilla's weaknesses, and harness their teamwork and strategic planning to confront the immense threat posed by the King of the Monsters.