you mean besides the half dozen times that exact same thing happened like i dont know KOREA. id argue Korea was at a just as great a disadvantage as mexico was in thier war against japan. didnt stop Yi from SHIT STOMPING the japs. there were literally battles were yi was taking just over a dozen ships against japanese fleets numbering in the 100s and not only beating them but outright annihalating them wholesale with little to no losses of his own. if one admiral can do that then i dont see why a general cant do the same.
First off, the Imjin War was less a demonstration of Japanese military might than of Joseon Korea's utter lack of preparations for naval invasions. The Japanese marched from Busan to Pyongyang in the span of a few months (almost the entire peninsula), then lost everything from Pyongyang to Seoul in the same amount of time (half of the peninsula). The war itself, despite nominally lasting 7 years, only involved maybe 3-4 years of actual fighting. Joseon forces, once organized and directed from their northern focused positions (as the Manchu were more of a historical threat than the Japanese at the time), were able to blunt the Japanese advance and push back once the Ming contributed forces. This is a far cry from Mexico's performance in the Mex-Am War.
Additionally:
1. Admiral Yi was highly successful but saying he singlehandedly defeated the Japanese is a bit of Park Chung-Hee era war hero worship propaganda. In terms of leadership, the Joseon kingdom also had General Gwon Ryul, Admiral Won Gyun, Admiral Yi Eokgi, and so on, all of whom were able to score vital victories against the Toyotomi forces. Mind, Yi Sun Sin also had a nasty habit of taking full credit from victories involving other admirals (Won Gyun, for example). Even without Admiral Yi, the Joseon still had a fair chance of survival.
2. As important as cutting off naval supply lines were, the Righteous Armies (made up of peasants, scholars, government officials, and Buddhist warrior monks) harried Japanese land forces, delaying them from total conquest until the Joseon armies could reorganize and Ming forces could arrive to assist.
3. The victory you mentioned there, the Battle of Myeongnyang, was in the second phase of the war, when Joseon survival was guaranteed. The Ming had already entered the war and the Japanese were unable to make even a quarter of their previous gains. While Yi's contributions were invaluable, Japan no longer had any chance of annexing Korea, let alone invading China. Absent Admiral Yi, the Japanese would still have been defeated.
Mexico, on the other hand, had no patron like the Ming were to the Joseon. They were not fighting for the continued existence of the state (Hideyoshi intended on taking over the peninsula, America was going after uninhabited territories), nor were entire villages torched, slaughtered, and abducted. The Americans weren't selling Mexicans into slavery or abducting them, thus engendering a huge amount of militancy amongst the Mexican populace which would lead to widespread insurgencies in the manner of the Righteous Armies.
It's not a one-to-one comparison you can make there. There's just way too many differences between those two situations.