What was the Filipino military tactics that were used during the Philippines War of Insurrection (1899 - 1902)?
First of all, one point that needs to be made is that calling this war an “insurrection” is a little bit questionable. The term “insurrection” implies a rebellion against a legitimate government. It is hard to see how the United States had a legitimate claim to rule the Philippines. This war is therefore often referred to as the Phillipine-American War.
With regard to your question, the Filipino military tactics were dictated largely by their inferior military power. The Filipino fighters were fairly numerous, but they were not well-trained or well-armed. They had not been a regular army under Spanish rule and therefore did not have the discipline or training of such an army. Perhaps more importantly, the Americans had superior fire power. They had such things as automatic weapons and artillery and gunboats while the Filipinos had, at best, small arms.
The Filipinos started by trying to fight a conventional war. They did things like trying to fight out of trenches as the US tried to break out from Manila to pacify the countryside. The Filipinos tried to fight in this way for a time, but then came to realize that they had no chance of victory through such tactics. Therefore, they moved to an attempt at guerrilla warfare. Aguinaldo and his forces tried to move around the countryside and inflict small and irritating defeats on the Americans. In this way, the conflict was something like the Vietnam War where superior American forces were trying to fight a conventional war against guerrilla forces that would not engage in major battles and which were hard to distinguish from the noncombatant population.
In this war, then, the Filipinos initially tried conventional military tactics but soon moved to guerrilla tactics against a vastly superior foe.