Order of Battle: When read carefully, this account has some interesting information about the nature of the battle between the Nephites and the Lamanites. We are told in verse 27 that the Lamanites were "being as numerous almost, as it were, as the sands of the sea." Additionally, the Nephites had pursued the Amlicites on the East side of the river, but they had managed to meet with the Lamanites and march on Zarahemla such that they were now approaching Zarahemla from the West side of the river. Alma and his troops are approaching from the East.
This difference in approach is significant, because it means that Alma has an entire army that must ford a river to reach the battlefield, upon which a vastly larger army was waiting. In conditions such as these, one might suppose a simple and overwhelming Lamanite victory. The Lamanites could occupy dry land, and simply wait for the Nephites to emerge from the river. With the higher and drier ground, not to mention the great superiority of numbers, this should have been an easy Lamanite victory. It was not.
Two facets of the Nephite attack are important. Undoubtedly the individual battles between Alma and Amlici and the king of the Lamanites are most significant. Equally as significant, however, is the information in verses 34 and 35. In those verses we learn that Alma's actions clear the way for his army to cross. In other words, not only is there a numerical superiority of the entire Lamanite force over the entire Nephite force, but that this numerical superiority was not brought to bear! The entire Lamanite army does not clash with the entire Nephite army. Alma fights with the leaders of the two factions of the Lamanite army, Amlici as leader of the Amlicites, and the king of the Lamanites.
What we have in these verses is a description of individual battle of kings as representatives of their armies rather than the battle between the armies themselves. If we accept the account before us, Alma crosses the river with some smaller number of men under his immediate command, and begins combat with Amlici himself. Out of all of the numbers of the Lamanites, so numerous as to be like grains of sand, Alma just happens to begin his battle with an opponent of equal social position in the opposing army. This could not have happened by chance. The order of this particular battle somehow called for combat by the king (or chief judge, in Alma's case).
Such a mode of battle is relatively rare, but certainly not without precedence. In the Old Testament we have the story of David and Goliath, where the entire outcome of a battle rested upon a battle of champions. Thus Alma is allowed to fight Amlici through to the conclusion of that skirmish without the rest of the Lamanite army being brought to bear. With the defeat of Amlici, Alma then continues to direct combat with the king of the Lamanites.
Verse 32 indicates that the king of the Lamanites withdrew and sent his guards against Alma. This indicates that he could have sent those guards prior to this point in time, and that the very presence of the king fighting with Alma must have been an arranged combat. With the defeat of the two leaders of the Lamanite armies, Alma secured sufficient victory to allow his army to cross the river.
Redaction: Once again Mormon's selection of the facts to present allows him to place Alma in a position where only his reliance on the Lord will save the day.
For Mormon, the point of the conflict is to demonstrate the power of the Lord, which he does by emphasizing the relative size of the two armies. When he has Alma attacking the opposing kings directly, once again Mormon paints Alma as an underdog, thus highlighting the miraculous salvation by the Lord.