The Spanish conquistadors in Pizarro's original force, as well as his reinforcements, were really quite unique.
We tend to think of the period as being characterized by monarchs and royal armies. Pizarro and his men were anything but a royal army. The bulk of them came from Extremadura: a remote, mountainous, and relatively poor area of Spain renowned for producing soldiers. Pizarro is, famously, Cortez's second cousin once removed, from this same region. If you were a young man of Extremadura during this period, soldiering was pretty much your best prospect for advancement, and Cortez was your hero. The reconquista and other conflicts had supplied several centuries of constant warfare that honed Spanish cavalry into the very best of Europe. The Extemadurans were the best of the Spanish. The stock that Pizarro's conquistadors were drawn from was elite.
Now, consider how that stock was drawn. As I mentioned above, Pizarro's force was no "royal army". No agents of the crown went to Extremadura and mustered up an army to send to Peru. These men paid their own way to the new world as an investment. With the reconquista finished and fabulous tales of conquest coming from Cortez's campaign, many soldiers willingly went to the new world to make a fortune for themselves. The men in Pizarro's company had already been on a difficult path before they set foot in Peru, but they were not just servants of the crown loyally following orders. They were entrepreneurs desperate to make good on their investment. Pizarro basically had his pick of the most ambitious men available.
One thing that made Spanish cavalry of this period so dangerous was pure reckless courage. If you put an overwhelming force in front of them they would charge directly into it while screaming, "Santiago!". The notion was that the enemy would not expect such insanity, and God would see them through anyways. The crazy thing is that this worked almost all the time in Peru. Pizarro's men were evil, greedy men, but they routinely routed enemy forces many times their size with reckless charges. On flat open ground, mounted conquistadors were virtually untouchable. The Incas learned this far too late.
The kidnapping and ransom of Atahualpa was an insane feat that typified the conquest of Peru. Pizarro's force was billeted in guest quarters that consisted of several long buildings with many doors facing a central square. They were surrounded by a royal Inca army dozens of times their size. They were too far from the coast to retreat if things turned violent, and they were convinced the Inca meant to turn things violent. For his part, the Inca saw the Spanish as a distraction from the more important task of mopping up the civil war that had just happened. The Spanish were too small a force to offer any serious resistance. After some scheming and diplomatic back and forth, Atahualpa and several thousand of his soldiers walked right into Pizarro's trap. They entered that courtyard and Pizarro's men rode out of every door of those long buildings, screaming. The expedition's cannons were fired for added psychological impact. The Inca's were compressed from all sides and panicked. Atahualpa was snatched from his litter and taken captive. The Spanish massacred thousands in the square and then continued riding down the Inca soldiers who hadn't been able to fit in the square for hours after Atahualpa's capture. With their command decapitated, there was little resistance.
As the conquest slowly progressed, the Inca resistance was typified by brilliant logistics, massive numbers, and flawed command that just couldn't seem to come to grips with what elite Spanish cavalry could do. The Spanish were taken by surprise and surrounded in Cusco by an absolutely massive army that appeared seemingly from nowhere... and didn't attack. The Inca commanders wanted to ensure they had an absolutely overwhelming force, so they continued to amass forces instead of attacking when surprise was on their side. They initially controlled the fortress of Saqsaywaman, but the Spanish were able to take it back due to the long delay in attack. That gave them a position to endure a long siege, which they did.
Some Inca generals did have success once they knew what they were dealing with. They learned to ambush the conquistadors in mountain passes, rolling boulders down on them from above. They learned to attack on rough ground that the Spanish horses couldn't be useful on. However, the Inca rulers seemed unable to comprehend that such a tiny force could offer resistance, so they still ordered their generals to offer pitched battles on flat open ground, which went against the Inca every time. These battles, such as at Lima, were tragically expensive for the Inca because their generals led from the front and often went into battle resolved to win or die.
Naked military force wasn't the only reason the Inca lost. The Spanish were adept at turning factions against the Inca's. The Inca empire was young and had been rapidly expanding. A lot of the people they had so recently conquered were only too happy to join the Spanish, not dissimilar to how the Aztec's enemies were eager to join forces with Cortez. The Inca empire was also predicated on worship of the Inca ruler as a living god. That became a serious flaw when the Spanish set up their own puppet Incas. However, while Cortez had a massive native army at his back by the time he reached Tenochtitlan, Pizarro's forces were often shockingly outnumbered but still managed to pull off seemingly impossible victories. Spanish cavalry really was that good if you fought them on their own terms, and the Inca chose to do that more often than they were ultimately able to afford. There were also other factors, like plague, that should not be underestimated.