Quests
Noita contains several hidden quests. These are more involved than simple puzzles and tend to span multiple biomes, if not multiple playthroughs.
Hand Statue Quest
In the Snowy Depths, several hand-shaped statues appear.
Kicking these statues (including with Telekinetic Kick) will spawn an increasing number of Munkki enemies. The third statue kicked will also spawn the Broken Spell.
In the Hiisi Base, the Hiisi Anvil can be used to repair the Broken Spell into Summon Portal.
In the Underground Jungle, there are four Munkki statues, each holding a staff either horizontally or vertically. Casting Summon Portal at the intersection of the lines formed by these staffs opens a portal to the Robotic Egg, within which are several robotic enemies, a wand, and a chest containing The End of Everything. Additionally, reaching the Robotic Egg this way for the first time unlocks Summon Omega Sawblade.
Sky Temples Quest Chain
Floating high above the surface, several mysterious temples can be found.
Initial Clues
In the far east of the Desert, the Watchtower can be found. At the top of the Watchtower a glyph can be found, depicting a structure in the sky above the Pond. This clues towards the discovery of the Ominous Temple.
Once discovered, the Ominous Temple has two stones with arrows near the top-right and top-left edges, pointing east and west respectively. These provide a hint for the existence of the Kivi Temple, and the Spirit Temple. The other sky temples have similar arrows, pointing to the next temple in that direction, if it exists.
Part 1
Above the Snowy Wasteland floats the Barren Temple, containing mysterious glyphs, a Potion mimic, and a book. The potion mimic can be charmed with Pheromone or other methods, allowing access to some Mimicium, which will be needed for part 2. The glyphs and book are hints towards later portions of the questline.
Part 2
Above the Giant Tree floats the Spirit Temple, containing many winding passages, several empty Potion mimics, some water, and some Pheromone. A glyph in the center room depicts ten bottles surrounded by hearts.
If you haven't charmed the potion mimic from the Barren Temple (or elsewhere, if you've been lucky enough to find one), the Pheromone pool can be used for that purpose. If you have, its Mimicium can be used to awaken its siblings. Each mimic awakened lights up one of the bottles on the glyph. Awakening ten will spawn and unlock the Sea of Mimicium spell.
Part 3
Above the Pond floats the Ominous Temple. Within is an odd chamber containing a small amount of Ominous Liquid.
Completely filling this chamber with Ominous Liquid (best accomplished by casting Sea of Mimicium, but any method works) will drop and unlock the Touch of Grass spell.
Part 4
With Touch of Grass, return to the Barren Temple. Casting it here, as hinted by the Grass glyph, will turn the temple's entire surface into Divine Ground, and drop and unlock Cessation.
Side Options
Above the Giant Skull floats the Kivi Temple. No unlocks or achievements are found here, but the Kivi presents a challenge that you may wish to overcome for its own sake.
The Kivi's max HP is equal to Minä's, and it automatically retaliates against all damage taken with equal or greater holy damage, making it very difficult to fight safely. The easiest way to avoid this retaliation is to use Cessation with lifetime increasers; hit the Kivi with damage over time or attacks slow enough that you can vanish before they hit it. Killing it spawns three Kummitus, also with max HP equal to yours; their wands and gold could be considered the reward for Kivi's defeat.
The Kivi Temple also contains a bottle of Beer, while the Ominous Temple contains a bottle of Milk. Mixing the two produces Molut. This one interaction is currently the only unique purpose for these three liquids, so for now it can be presumed that they exist solely for humor value.
Unsolved Mysteries
In the Parallel Worlds, mysterious arrangements of eyes can be found. They appear to be a cipher of some kind, but they have yet to be decoded.
Buried near the Hiisi Base is a mysterious room containing a mysterious structure and a cauldron, which may or may not contain some Void Liquid depending on the date. The purpose of this room is unknown, and it has been suggested that this quest may not be yet fully implemented.