Olmec has 3 different phases he will enter depending on which floor of their arena he's on.
On the entry floor, Olmec's first phase is similar to how he acted in Spelunky HD. However, compared to his behavior in Spelunky HD, Olmec is much faster and does not spawn enemies unlike the Spelunky HD or Spelunky Classic. When the player is close, he will jump up above the player and pause for a second before coming down, killing the player instantly if they are caught underneath and destroying the tiles of under him.
Olmec's second phase triggers once the he falls into the second floor. He will begin to levitate, revealing two purple jets beneath him. He will then move in one direction until a block or wall impedes his movement, upon which he will switch directions. Periodically, his face will open up horizontally across his eyes revealing two seemingly mechanical eyes underneath, and will then launch 3 bombs at varying speeds from both sides of his face. Olmec's jets aren't immune to damage, and take three HP of damage before shattering. Upon breaking both of the jets beneath him, he will fall down until he hits ground, crushing two rows of tiles upon landing. If he hits the third floor, he will go to his third phase, though it's possible for him to simply die in this phase as well if he falls directly into lava.
Olmec's third phase is similar to his first one. He will jump above the player, pause, then come crashing down. However, in-between jumps, he may also open his head similar to in his second phase, and unleash a UFO from both sides.
At the bottom of his lair is lava that he can fall into, and die.