Despite the ideas of Manifest Destiny, Walker was initially backed by the Liberal forces of Nicaragua against the conservative Legitimist forces. The liberals only abandoned their support of Walker in June 1856 once it was clear he was losing to Costa Rica. Similarly Walker only declared himself President and openly began pandering to the American south (legalizing slavery and other means) during July 1856, after he'd lost all domestic support in Nicaragua. Before that Walker had claimed 'merely' to be general of Nicaragua's army and military advisor to the president, as well as a naturalized Nicaraguan citizen. In reality he was power behind the throne, yet not one who could act unilaterally without losing support.
To win the Fillibuster War, Walker needs to maintain his liberal support since most of his army is Nicaraguans. In 1855 he actually had some popularity due to ending the Nicaraguan civil war without conducting reprisals and due to maintaining discipline in his forces. With his limited resources success leads to further successes as it builds his reputation, while defeats will put the Fillibusters in a downward spiral.
I'll offer a simple POD. During the Second Battle of Rivas, Walker enveloped the city in a surprise attack which caught the Costa Rican army completely off guard. Both Walker and Costa Rica attribute the Fillibuster defeat to the fact Colonel Jose Machado was killed by a Costa Rican sharpshooter while supporting an attack on the headquarters in the city. So the POD is the bullet misses, and Colonel Machado leads his column of Nicaraguans to overrun the Costa Rican command early in the battle.
Present at the Battle of Rivas at the headquarters was the President of Costa Rica, Juan Rafael Mora Porras, personally commanding the war. The president's brother and brother in law as his generals and major political allies, and the ranking Commanding General of the Costa Rican army (OTL the latter died in battle at Rivas anyways though).
Caught by surprise, encircled in Nicaraguan territory, with their command and arsenal captured in the early stages of the battle, and demoralized, the Costa Rican army at Rivas will likely surrender in quick order with minimal casualties to the Fillibuster and Nicaraguans (combined they had relatively equal numbers to the Costa Ricans). Walker's March invasion of Costa Rica was a disaster, but at Rivas that's essentially Costa Rica's field army captured in their counter invasion within the first two months of the war, along with the political leadership.
There's no way Costa Rica's present government would survive that. Mora Porras had a lot of political enemies back in Costa Rica. In fact despite being a national hero who defeated the hated William Walker, he himself was overthrown in a coup two years after the end of the Fillibuster War. And despite being a liberal state as well, the Costa Rican republic had recently taken measures to disenfranchise the majority of the population and other measures against the peasants. This is factionalism that Walker can take advantage of. Especially since like with his recruiting of former opponents in Nicaragua, lenient treatment of the captured Costa Rican prisoners and officers would lead many to join him. If Walker marches south after a victory at Rivas, there is a very good chance that Costa Rica would end up as a 'sister republic' to Nicaragua. Or be so embroiled in their own civil war that the southern front of the Filibuster War is essentially closed. And a complete victory like that would secure Walker's position domestically. At the start of the war the Nicaraguans saw Costa Rica as the aggressor and were willing to fight them. Indeed after Walker was overthrown, the allied Nicaraguan forces instantly conflicted with Costa Rica stealing their territory. Here the Nicaraguan unity government estbalished by Walker has no reason to dispose him, as he is winning wars for them.
OTL the Costa Rican campaign occurred from March to April 1856. Guatamala, Honduras, and El Salvador did not declare war until July, and didn't go on the offensive until Sept/October. Here, the removal of the southern front changes the war entirely. Without Costa Rica, the Central American Allies are unable to cut off the Fillibuster's connections on the San Juan river, despite Vanderbilt's attempts. No defeats means the Nicaraguans aren't deserting from Walker's army, making him less dependent on southern support and meaning his plans regarding slavery and white rule are postponed until after the war is won. No threat on Nicaragua's southern border means Walker can concentrate Nicaragua's army in the north, with greater numbers than they had OTL, and the Costa Rican army if they're playing a part are more likely to be fighting alongside Walker.
The main issue at this point is despite being a certified academic genius (Really. William Walker got his law degree at 14, with a second degree in literature, and a medical degree by 19. and threw it all away because his fiance died and he hated his dayjob), Walker has no military training and was actually kind of a terrible tactician. He displayed some qualities of generalship in terms of strategy, leadership, and discipline. But tactically he had a tendency to have his army attack fortified cities held by equal or greater numbers of allied forces, relying on surprise and elan to win. And he did this repeatedly throughout his career.
Still the situation as it is now, with only a one front war, should be winnable by even a moderately capable leader. Walker's opponents Guatamala, Honduras, and El Salvador were all conservative governments that recently overthrew liberal governments through coup, civil war, or invasion. In fact Guatamala had previously invaded both Honduras and El Salvador to conduct regime change, in the case of Honduras only a year prior (at the same time Walker was invading in the Nicaraguan civil war). With the allied invasion having been prompted by the invitation of Nicaragua's conservative party, Walker could easily spin this as Guatemala being up to its old tricks and maintain legitimacy with his local army by claiming to be the legitimate defender of Nicaragua and Costa Rica's liberal governments.
The prior wars between the Allied Central American Army meant they were less unified than they should be. The Guatamala and El Salvador commanders feuded with each other and left themselves open for a defeat in detail at the simultaneous battles of Masaya and Granada (and featured another case of one of the allied army leaders needlessly exposing themselves to danger on the battlefield which could have gone horribly wrong). The main reason they weren't was that Walker was down to a few hundred men at that point OTL. The predominantly liberal El Salvadorian army commanders were anti-American and commited to the war against Walker, but the conservative government back in El Salvador distrusted the army leadership and suspected they were planning to conduct a military coup once they returned to El Salvador (which they were). In Honduras, the ousted general and president Jose Trinidad Cabanas OTL offered his services to Nicaragua if they would restore him to the presidency, and brings with him a lot of connections. And all of the Central American allies were military ruled states. None of them want a long war as a big defeat or committing too many forces could bring down their governments.
So with the change of a single bullet at the battle of Rivas, the Fillibuster War could very possibly be won by Walker, provided some luck, smart politics, and good PR. By playing divide and conquer its not impossible that by 1858 Nicaragua, Costa Rica, and Honduras are ruled by governments established by Walker and their armies commanded by him, who's considered a national hero and unstoppable military leader by many. Particularly in Nicaragua, where he has just lead them to stomp on all their neighbors. They might even consider it the Nicaraguan War of Independence against their neighbors. Additionally at the time and until 1900 there was even still some sentiment for the Republic of Central America, who's supporters would be seeing William Walker as their unifier.
And then things are gonna get real spicy once William Walker is formally elected president and begins implementing his domestic agenda. Which imo even OTL did not include plans for US annexation, but was still tied to slavery and as controversial.
