In terms of mythological or religious monsters, there is Tlaltecuhtli, the "Earth Monster." She is a giant crocodile who lived in the primordial waters before our world was formed. At the dawn of the current age, the gods Tezcatlipoca and Quetzalcoatl tore her asunder, using half of her body to form the sky and the other half the earth. In another version of this story, Tezcatlipoca lured her to the surface using his foot as bait, Tlaltecuhtli bit onto his foot, but injured her jaw in the process, and thus was unable to descend back into the depths and was then able to be sundered into the land. This is why Tezcatlipoca is often depicted with a skeletal foot.
There are also the Tzitzimime, fearsome women who lived among the stars. Every 52 years the Aztec's calendars (they had both a 260 and 365 day calendar) would make a full rotation back to the day they started. On this occasion they would celebrate the New Fire ceremony, which involved all fires being extinguished and then a single fire being started in the chest of a sacrifice atop a specific hill outside of Tenochtitlan. If this fire failed to light, then it signaled the end of the world as the tzitzimime would descend from the sky and devour the people. In fact, it was thought that women at this time might change into fierce beasts and join the tzitzimime, and so were secluded inside during this part of the ceremony.
Moving away from mythology, there's a fairly well-known creature called an ahuitzotl which lived in the water and looked somewhat like a dog, but with grasping hands like a raccoon or monkey, and a long tail with a human hand at the end. The creature used the tail to lure people out to it and then seized hold of them, dragging them down and drowning them. The ahuitzotl would then eat the victim's eyes, teeth, and nails before letting the body float back to the surface. There's a great video on this beast from Invicta which sums up the primary source material, and has some historical (and not so historical) depictions of it.
Another monster was the tlilcoatl a giant black snake described by Sahagun as some 6 feet in girth, very long, and with a forked tail. It mostly hunted fish, but sometimes a foolhardy person would try to steal some of its cache of fish. The tlilcoatl would then chase after the thief and, coiling itself around him and inserting its forked tail into his nostrils (or anus), squeeze the life out of him. This fearsome creature was also said to be able to spit venom which would render a man stupefied and stumbling as if drunk.
The Aztecs also had numerous superstitions about terrifying creatures haunting the night. Famously, the goddess Cihuacoatl was said to sometimes walk at night weeping and wailing, and seeing her was an omen that war was coming. More prosaically, people going out to urinate at night were warned about seeing a hunched and squat figure with long hair, like a misshapen female dwarf, whose appearance foretold something terrible, even death, about to happen to those who saw her. People were also afraid of a severed head which might spring out and bite people in the calf at night, or seeing a figure bound up in funeral wrappings moaning and groaning in the dark.
A common theme with these night terrors was that a brave person might try to capture them, and thus defuse their ill fortune. Attempts to capture the apparitions listed above, however, would always be futile. The dwarf and the head would only bound away, mocking them attempts, and the moaning body would turn to clods of dirt in the hands of those who seized it.
If a brave person saw a giant at night, however, they could avoid the misfortune it foretold (death or capture in battle) by grabbing it and refusing to let go until it promised him valor in battle. Likewise, seeing a bundle of ashes rolling and billowing by meant death in war or sickness (or some generic misfortune), but that could be avoided by grabbing hold of it and demanding it speak (how one grabs hold of a bunch of ashes blowing in the wind is beyond me). There was also the "night axe" a headless corpse with its chest split open that went wandering the night, its rib cage clapping together like the sound of an axe chopping wood. While a brave person could seize it and demand promises of success and riches, a less stalwart individual might only pull out its heart and run off, wrapping it up and burying it. If, the next morning, the heart had turned into downy feathers, or thorns, then that person would have good luck. Unearthing rags or a piece of charcoal, however, foretold poverty and misery.
Of course, if you asked the Spanish, the whole pantheon of deities and spirits among the various Mesoamerican peoples were nothing but devils and demons, but what do they know?
Markham and Markham 1992 The Flayed God: The Mythology of Mesoamerica
Sahagun General History of the Things of New Spain, Book 5 and Book 11, trans. Anderson and Dibble.