Atlas does not spawn on its own, and requires the player to summon it with the Stone Fist. It can be summoned anywhere, at any time.
Atlas is a relatively slow boss, who lets its arms do most of the physical attacking. Atlas' arms cannot be damaged. Upon being summoned, the sky will immediately turn a fully opaque gray, and a message will appear in the chat: "The earth is trembling". Atlas spawns far above the player, drops down an arm as a surprise and shakes the screen which is completely visual, and then floats down to the player's level, beginning the fight. It fires out Prismatic Bolts, among many other projectiles.
It swings its arms at the player, attempting to deal damage.
Atlas fires Prismatic Bolts at the player, as a projectile.
At 75% health, Atlas summons 5 Cobbled Eyes in near proximity to itself, and begins to fire Miracle Beams alongside the Bolts. Its arms swing farther and faster.
At 50% health, Atlas summons 10 Cobbled Eyes in near proximity to itself once more. Miracle Beams are fired much more often, and its arms swing even faster and farther.
At 25% health, Atlas summons 20-30 Cobbled Eyes far away from itself.