Over 120 rare items in one video, sorted by level. It's virtually guaranteed to help you work towards your King of Katamari Damacy trophy/achievement. Plus, it's beginner friendly and contains no omissions or edits.

Resources:
http://fanboy.net/games/kd/
https://gamefaqs.gamespot.com/ps2/918766-katamari-damacy/faqs/36129
https://www.speedrun.com/katamarireroll/thread/7do2m

Thanks to Grass and Martini for the latest speed routes I used between the elements.

To reach the Eternal Levels, you must first complete the game (by completing Make the Moon). Then unlock each level as follows:
Eternal 1: 1.30 m in “Make a Star 4”
Eternal 2: 25 min. in “Make a Star” 8
Eternal 3: 800m in “Make the Moon”

Remarks:
– You must complete the level with the items to add them to your collection.
– The 4th step is not in the same place as in the original game.
– Some items are faster/easier to get in the North Star level, but you can't see your diameter.
– The four rings randomly appear in two locations: Eternal 2 (shown here) and Make a Star 2 (in the ring box). With Eternal 2, it's quicker/easier to get all four because you can stop immediately after each one.
– To my knowledge, elements marked with * only appear in one level.
– Text in brackets [ ] was added by me.

Use these handy timestamps to find exactly what you're looking for:

Make a Star 1 – 0:00
*Gold coin – 3 cm 8 mm 0:18
*Brown pencil – 5 cm 6 mm 0:41
Switch – 7cm3mm 0:58
*Red pencil – 4 cm2 mm 1:17

Make a Star 2 – 1:24
*Beige coloured pencil – 5 cm 1 mm 1:41
*Lime stick – 5 cm 2:02
*Pink crayon – 4 cm 8 mm 2:16
*500 yen coin – 4 cm 2:37
*Salmon – 16cm5mm 4:06
*Jam – 14cm 4:19

Make a Star 3 – 4:35
*Green pencil – 5 cm 1 mm 5:51

Make a Star 4 – 6:05
*Black pencil – 3 cm 7 mm 6:20
*Ochre pencil – 5 cm 7 mm 6:34
*Aqua Crayon – 5cm 4mm 6:59
*5th step – 84cm2mm 10:16
Goal lamp – 52cm3mm 10:40
Nameplate – 23 cm 7 mm 10:57

Make a Star 5 – 11:05
*Blue crayon – 5 cm 11:15
*Gold medal – 9cm7mm 11:43
*Sign for older drivers – 13 cm 6 mm 13:10
Steel cover – 57 cm 5 mm 15:20
Iron cover – 59 cm 9 mm 15:27
Concrete cover – 60cm1mm 15:33
*Sushi commercial – 30 cm 9 mm 16:02
Video game – 38 cm 7 mm 16:41
Bird's Nest – 94cm6mm 18:15
*Candy container – 37cm1mm 19:18
*Clapboard – 26cm1mm 19:29
*Accident report – 61cm3mm 19:37
*Encyclopedia – 35cm8mm 19:54
*8th step – 90cm3mm 20:39
Telephone pole advertising – 79 cm 9 mm 21:17
Clothes hanger – 1m42cm5mm 21:34

Make a Star 6 – 21:43
Draining board – 42cm 23:15
*7th step – 88cm4mm 24:05
School sign – 1m55cm2mm 25:37
Russian Doll (S) – 1m29cm1mm 26:06
Russian Doll (M) – 1m64cm4mm 26:12
Russian Doll (L) – 1m99cm6mm 26:16
Russian Doll (XL) – 2m34cm8mm 26:23

Make a Star 7 – 26:31
*4th step – 81cm9mm 27:33
Bathhouse Curtain – 93cm7mm 29:34
*/"Katamari/" Shield – 1m48cm1mm 30:00
*/"Experience/" [characters] – 1m48cm1mm 30:06
*/"In/" [characters] – 1m48cm1mm 30:07
/"Progress/" [characters] – 1m48cm1mm 30:08
Monument – 3m84cm8mm 32:11
Panda Sign – 6m58cm4mm 32:17
Totem Pole – 9m26cm7mm 33:36
Gym Storage – 9m 60cm 35:34

Make a Star 8 – 35:43
*Purple crayon – 5 cm 4 mm 36:02
*2nd step – 83cm4mm 40:40

Make a Star 9 – 40:49
Garden Rocks – 81cm4mm 43:46
Spirit of Joy – 3m56cm3mm 44:38
*Top [Step] – 91 cm 7 mm 44:53

Making cancer – 45:13
*Picture Story Show – 63cm9mm 49:47

Making Corona Borealis – 49:55
*6th step – 86cm3mm 51:10

Make Cygnus – 51:25
*Cuckoo – 12cm5mm 51:43
*White crayon – 5 cm 9 mm 52:00

Make the North Star – 52:25
Garden stone – 81cm4mm 53:00
Bathhouse Curtain – 93cm7mm 54:30
Monument – 3m84cm8mm 55:34
Panda Shield – 6m58cm4mm 55:44
Totem Pole – 9m26cm7mm 56:07

Make Fish – 56:17
*10th step – 94cm 57:33
Christmas tree – 2m3cm7mm 58:30

Make Taurus – 58:39
*Sweet Cow – 3m19cm6mm 1:00:18

Do the Big Bear – 1:00:27
*Spirit of Wrath – 3m56cm3mm 1:02:17

Make Virgin – 1:02:25
*3rd step – 84cm5mm 1:02:50

Forever 1 – 1:02:56
*Gold pin – 5cm 9mm 1:03:32
Foreign coin – 3 cm 6 mm 1:03:38
Checkbook – 10 cm 4 mm 1:04:20
Old coin – 5 cm2 mm 1:05:22
Roach Motel – 23cm 7mm 1:06:25

Forever 2 – 1:06:30
Diamond ring – 7 cm 3 mm 1:07:01
Emerald ring – 7 cm 3 mm 1:07:47
Ruby ring – 7 cm 3 mm 1:10:32
Sapphire ring – 7 cm 3 mm 1:12:32
Coffee milk – 19cm9mm 1:13:31
*Crayon box – 19cm4mm 1:13:57
Cream puff advertising – 30 cm 9 mm 1:15:15
Yellow color – 29 cm 1:15:33
[Yellow] Brush – 13cm 1:15:42
Local Police Sign – 70cm5mm 1:17:05
[Blue Garbage] Bucket – 1m26cm2mm 1:19:04
Umbrella Shop Sign – 1m14cm9mm 1:20:00
*9th step – 92cm2mm 1:20:25
Goal lamp – 52cm3mm [on top of] Goal post – 1m55cm4mm 1:20:40
Torn Shoji – 1m31cm 1:20:51
Monument – 2m71cm9mm 1:22:16
Weather vane – 2m87cm1mm 1:22:54
Eagle – 1m51cm1mm 1:24:53
Water tank sign – 1m94cm7mm 1:26:02
City map – 2m44cm5mm 1:26:16

Eternal 3 – 1:26:28
Fan – 50cm8mm 1:26:40
Lionpaw – 2m58cm 1:28:17
Shop sign – 7m45cm 1:31:45
Dentist shield – 8 m18 cm5 mm 1:32:02
Company sign – 6m2cm6mm 1:32:25
Hotel sign – 6m74cm5mm 1:32:45
Sperm whale – 17m80cm8mm 1:33:34
Satellite – 18m66cm2mm 1:35:00
Crane scaffold [L] – 34m80cm9mm 1:35:37
High School – 55 m61 cm6 mm 1:36:39
University – 63 m33 cm1 mm 1:37:30
Takeda Residence – 90 m54 cm2 mm 1:39:40

For more information, see the pinned comment!

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