For steam achievements lol.
Actually one don't need to collect every items to get all steam achievements.
So it is more likely a self-fulfilling challenge to 100% this game
--- to collect all the 109 stars and 12 gems per type.
And some extra ending themes as a prize from the developer.

ps: As @Ceremony in the comments pointed out, there might be 13 keys left after completion, however I cannot confirm which the key or door is missed. So the keys are not contained in the guide.

Update: Stars in Snake Island corrected from 11 to 10, thanks for @Blinky & @Darwoon pointing it out.

It takes two steps to reach the ending.

In the four main islands (achievements will jump out when you step in), collect 6 corresponding elemental gems and meet the great spirit (they're at room C0 for earth, water & fire island, room C2 for air island).
The small elemental are necessary for collecting many stars, so after you arriving new island, the first thing recommended to do is to meet the giant elemental, grab the rune in the same room, then collect the gem to awaken the elemental on the island.

After the last elemental is awakened, a portal to the initial island will be opened below the great elemental. Step in you can go back to the elemental seal on the initial island -- it's now open and allow you going north to Sanctum. (Or you could choose not using the portal but going back through turtle whenever you like.

Opened Sanctum Gate

Sanctum is a 3x3 area with no map. The quiz at its four corners must be solved to unlock the gate at the center room. To solve the quiz, make the right-type elemental interact with the 2x2 big crystal in each room.
The right elemental types are implied by
The emblem on the gate
The theme of the room
The quiz in Sanctum might be difficult and have multiple solutions, so don't be frustrated if you take much long time to solve them.

After all four crystal quiz solved, you get the access of the top room of Sanctum, go there and enjoy the ending theme. You can end the game anytime you like and continue the game from Sanctum afterwards without losing your progress

Strongly recommend to collect the items helps you make more progress before collecting stars and all the gems.
It contains two parts:
The runes --- can make you unlock the corresponding type (can distinguish by color of emblem) of color blocks.
The upgrades --- can give you extra moving power to discover the world.

The earth, water, fire and air runes are located in the same room with the corresponding giant elemental. (C0 for earth, water, fire and C2 for air)
The tree (green) rune is located on the 'small tree island' just below the initial island.
The snake (dark purple) rune is located at the top room of the snake island.
All six rune can be acquired with no upgrades or elemental awakened.
So when you get stuck, find rune first, then consider the elemental or upgrades.

I guess it is possible to get all the upgrades without awakening any elemental, but I'm not sure.

The Glove in Stone Cliffs
Can make you dig through dirt block
The glove is located at room underground-C1, to get it the gate at room underground-C2 must be opened.
Tips: Look at the set-up in the front of the gate. Find the same set-up on the ground. They're at the four corners of the island, each has one movable crate. Don't know the emblem of the crate? Move it to random pit and have a look from another corner room.

The Flipper in Tidal Reef
Can make you swim through water tile except deap ocean
The flipper is located at room A4, to get it the dragonfly puzzle must be solved.
Tips: Find three dragonflies on the islands at other three corners. Chase each until they disappear, record their color and path. Imagine the 5x5 grid at A4 as the map of the island, the crate as dragonflies Push the crate to corresponding start point (three corners) and use them to repeat the paths of dragonflies.

The Armor in Raging Volcano
Can increase your heat gauge from 4 to 6
The armor is located at room E0, to get it three red keys must be acquired.
Tips: Keys are acquired through boss-encounter at room A0, A4, E4 (Three corners again haha) The spawn enemies are random so no fixed walkthrough. I tend to banish the enemy who cast tracking flame first. Alert the bomb of slime can push the seal to somewhere you cannot reach.


The Wings in Frozen Spire
Can make you slide straightly over 1-tile-wide hole
The wings is located at room A0 where can only be accessed by birds, and the bird connection is random between save-files. To get it the blue key must be acquired.
Tips: Check the other three corners, there are three 'small house'. The patterns on the doors are the map of the island. At each indicated room, there is one tile with different floor pattern. Check it and you'll have an egg, take three eggs to the birdnests you'll get the key.

The number of stars on the four main islands will not be mentioned, because they're shown on the in-game map. (Maybe I'll recount them later...) But I will list the puzzle-source stars and give maps to tell which rooms one may access. (Hints of those puzzles might be added later... Actually the tiles in the puzzle room itself usually give many clues.)

Stars: 3 (One behind the gate of Sanctum so not shown on the map)

Seal quiz at A2
Instrument quiz at D1
Earth Gems: 10
Black Gems: 2 (1 behind the seal at A2, 1 behind a hidden passage)
Extra tips: 1 star underground needs flipper
Extra tips: Some walls underground can be broken.

Instrument quiz at D1
Water Gems: 10
Black Gems: 1 (1 behind a hidden passage)
Extra tips: 1 star needs wings, and 1 star behind a waterfall
Extra tips: The changing water level might open some paths.

Statue quiz at D4
Instrument quiz at B3
Fire Gems: 10
Black Gems: 2 (1 behind the statue quiz at D4, 1 behind a hidden passage)
Extra tips: 2 stars need to build a bridge to the neighbor room
Extra tips: The exploding crate can push away and ignite neighbor crates.

Bird connection might be different.
A1 is just an empty room in current version.
Instrument quiz at D4
Air Gems: 10
Black Gems: 1 (1 behind a hidden passage)
Extra tips: 1 star need to fly over hole and reach a secret staircase
Extra tips: Fall into a wooden crate from high place can destroy it.

The top room is sealed by four elemental rune.
Awakening at the top room needs 9 black gems.
Black Gems: 1
Stars: 10

Corresponding upgrade and elemental awakening might be necessary.
Each has one giant bell locked by grass rune.
Corresponding Elemental Gems: 1 each island
Black Gems: 1 each island
Stars: 3 each island (1 by knocking the bell)
Extra Tips: Some islands can be landed from opposite direction.

No requirement.
Stars: 1

Knock all four giant bells to unlock the gate.
Unlock the giant bird travel. (BTW, I unlock it after acquiring all the gems and only stars on the snake island left, lol)

Stars: 1
Black Gems:1 (behind a secret passage)

Gems: 4 (each elemental 1, all upgrades needed)
Stars: 7

Stars: 1
Tips: Look at the mountain mark between the rocks at top-right.
A room in Stoney Cliffs has the same mark.
It's room B3. Put the crates the same as B3.
It seems the additional crate doesn't need to be pushed to the ocean, just leave it alone outside center area.

Indicate a secret passage is near, push somewhere to trigger a wall explosion clearing new path. (Though the hidden path might merely a path and lead to nothing special.
Some hidden things might not be hinted by either the mark or the snake, so be brave to try when seeing something out of reach.
Land-edge like this at the screen-edge, though looked like a dead end, can usually be passed to neighbor room. Be ware!