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I found a really good guide on Youtube by MXE VIDEOS for any that do not want to solve puzzles by themselves. It is made for the PS4 version, but it is exactly the same on all consoles.

Just to note though, there was an update after he made the video that changed the game a little.

This starts at 24:42 - 26:26

You need to move the shadows of the chandeliers so that the right one is a stepping stone, and the left one leads you to get onto the left side of floor 3. Then you pull the fire alarm on floor 3, and the shadows go up higher. Then from the right side, jump on the shadows, jump to shadow of right chandelier, then jump to middle platform with luminary, and finally on to floor 4. After that the video is fine again.

Full Walkthrough :
Timestamps:

00:00 Intro
00:24 Act I: A New Dimension, Illuminated Achievements (Collectible 1,2,3)
02:31 Act I: Not That Kind Of Game! Achievement
02:42 Act I: To The Heroes Among Us Achievement
03:19 Act I: Room 529 Achievement (Collectible 4,5,6,7)
06:50 Act I: Now That’s Thinking With Shadows, My God, It’s Full Of Stars! Achievements (Collectible 8)
07:56 Act I: Punching Bag (Collectible 9)
09:08 Act I: You Broke My Finger!, A Carousel Of Broken Dreams Achievements (Collectible 10 – Streets Sweeper Achievement)
12:50 Act II: The Family Life Achievement (Collectible 11)
13:12 Act II: This Circus Is A Disaster Achievement (Collectibles 12,13,14)
17:39 Act II: The Cyclops’ Bottle Achievement
17:49 Act II: Just Like Harry Achievement
19:03 Act II (Collectible 15)
25:53 Act II: No Backpack Bird Needed Achievement
26:11 Act II: Handy Person Achievement (Collectible 16 – GroundsKeeper Achievement)
29:12 Act III: How’d you get in Achievement (Collectible 22,26,19)
33:36 Act III: Let There Be Light, FIN Achievements (Collectibles 20, 21,18,23, 24, 25, 18 – BookKeeper Achievement)
40:58 Streets Sweepers Achievement
42:06 GroundsKeeper Achievement
42:51 BookKeeper Achievement