The Yaaxil are protectors of the Silver Box of Ix Chel. They roam the subterranean temples and the jungle surrounding Paititi, where they attack anything they perceive as a thread. It seems that over time their presence has influenced (or even started) the myth of the Pishtaco, a two legged forest-dwelling creature, not much unlike a Sasquach or a Yeti. When Lara Croft tells Abby Ortiz about her encounter in the jungle, she thinks Lara is trying to "pull her leg".
Later in the game Lara crosses paths with the Crimson Fire when she is searching for the Silver Box in the temple. Here open hostilities erupt, especially when the Yaaxil discover that the Silver Box has been taken from its hiding place.
Shortly before the end, Lara allies herself with the Yaaxil and Crimson Fire in order to defeat Trinity and Dr. Dominguez, who has at this point the Silver Box of Ix Chel and the Key of Chak Chel in his possession and has already started the ritual to renew the world.
The Yaaxil live in and around Paititi's many abandoned temples. They seem to prefer to live under ground and only come out to strike at their enemies.
When exactly Lara meets the first Yaaxil is not easy to say, as they - at first - mostly keep to the dark corners of the surrounding jungle and only attack the Trinity soldiers on patrol, e.g. after leaving the Cenote. Lara doesn't even know their name by this point.
One of the earliest occurrences is during the Underworld Gate challenge tomb, where the Yaaxil will throw boulders at Lara and try to scare her off. One of them can be seen up on a ledge above the turnable mechanism with the rope coil. If Lara visits the tomb after finding out about the Yaaxil, she will yell "You don't scare me. I know what you are." at them.
The Yaaxil are quite agile and attack with their claws in close combat, while their archers shoot at Lara from a safe distance. It is advisable to get to a place where the archers can't reach her - like behind a pillar or wall, or even better under a roof - while also not being too crammed in, so that Lara has enough space to move when the ground troops attack, which she should probably get rid of first.