Note: Unfortunately, most of the achievements didn't unlock for me in the video, probably because I used save backups, which caused the cumulative achievements to break and subsequently disrupted the rest of the achievement unlocking sequence. I have roughly placed timestamps where you should obtain the achievements, but the timing may not be very accurate. However, in this video, the game is completed 100%, and that should be sufficient to unlock all achievements.

Clickable timestamps can be found in the pinned comment on YouTube.

Intro
03:39 - Achievement Helpful

Chapter 1: The Dark Forest
04:09 - Litter [1/131]
06:53 - Litter [2/131]
07:01 - Lost Kid [1/40]
08:19 - Litter [3/131]
09:35 - Clothing [1/118] - Brimcap
13:43 - Clothing [2/118] - Custom Tee
18:54 - Lost Kid [2/40]
19:12 - Lost Kid [3/40]
19:23 - Lost Kid [4/40]
20:21 - Clothing [3/118] - Headband + Achievement Kitten Caboodle
20:55 - Clothing [4/118] - Beanie
21:03 - Litter [4/131]
21:07 - Clothing [5/118] - Stripey Tee
22:00 - Clothing [6/118] - Flower Dress
22:17 - Litter [5/131]
22:22 - Clothing [7/118] - Starry Tee
22:48 - Clothing [8/118] - Bow
23:05 - Clothing [9/118] - Sunhat
23:14 - Lost Kid [5/40]
23:38 - Clothing [10/118] - Hoodie
23:47 - Litter [6/131]
24:06 - Clothing [11/118] - Scarf
24:21 - Lost Kid [6/40]

Chapter 2: A Wielder's Duty
30:08 - Clothing [12/118] - Cord Coat
30:39 - Clothing [13/118] - Round Glasses
31:10 - Clothing [14/118] - Moon Tee
33:07 - Clothing [15/118] - Pocket Jacket
35:03 - Achievement Meet Your Hero
37:47 - Clothing [16/118] - Black Dress
38:13 - Clothing [17/118] - Big Star
39:09-41:02 - Clothing [18/118] - Kerchief
44:26 - Litter [7/131]
48:04 - Litter [8/131]
50:18 - Lost Kid [7/40]
58:16 - Art Class [1/20]
59:34 - Brush Style [1-4/25] - The Brush Style Starter Kit
1:01:55 - Art Class [2/20]
1:06:13 - Litter [9/131]
1:06:19 - Lost Kid [8/40]
1:07:03 - Brush Style [5/25] - Custom Brush Style
1:08:23 - Lost Kid [9/40]
1:08:55 - Brush Style [6/25] - Paint Bucket
1:09:19 - Lost Kid [10/40]
1:11:13 - Litter [10/131]
1:12:54 - Litter [11/131]
1:12:58 - Clothing [19/118] - Cute Dress
1:13:10 - Lost Kid [11/40]
1:14:06 - Lost Kid [12/40]
1:14:18 - Clothing [20/118] - Flower
1:14:40 - Litter [12/131]
1:14:46 - Clothing [21/118] - Howdy
1:15:09 - Clothing [22/118] - High Nooner
1:15:25 - Lost Kid [13/40]
1:15:36 - Litter [13/131]
1:16:00 - Brush Style [7/25] - Dots
1:16:27 - Clothing [23/118] - Hotneck
1:17:18 - Litter [14/131]
1:17:29 - Clothing [24/118] - Big Heart
1:19:18 - Litter [15/131]
1:20:14 - Litter [16/131]
1:20:51 - Litter [17/131]
1:21:10 - Lost Kid [14/40]
1:22:43 - Decor [1/100] - Classic Painting "Here in the Garden"
1:30:34 - Achievement Phone Call
1:38:07 - Clothing [25/118] - Black Tee
1:33:35 - Clothing [26/118] - Beret
1:36:36 - Brush Style [8/25] - Stripes
1:37:04 - Clothing [27/118] - Wielder Cloak
1:37:27 - Litter [18,19/131]
1:38:17 - Litter [20/131]
1:39:16 - Clothing [28/118] - Smock

Chapter 3: Portraits of Chicory
1:44:46 - Clothing [29/118] - Wielder Wrap
1:46:01 - Brush Style [9/25] - Diamonds
1:46:44 - Litter [21/131]
1:49:51 - Litter [22-24/131]
1:55:27 - Decor [2/100] - Chicory's Portrait + Achievement Muse
1:59:17 - Decor [3/100] - Sweet Set
2:00:55 - Lost Kid [15/40]
2:01:04 - Clothing [30/118] - Sparkles + Achievement Clothing Curious
2:01:21 - Lost Kid [16/40]
2:02:46 - Lost Kid [17/40]
2:04:57 - Clothing [31/118] - Gardener
2:05:10 - Litter [25/131]
2:05:27 - Clothing [32/118] - Leafy
2:05:48 - Lost Kid [18/40]
2:06:01 - Clothing [33/118] - Fungus
2:06:33 - Lost Kid [19/40]
2:06:42 - Litter [26/131]
2:07:05 - Brush Style [10/25] - Flower
2:07:36 - Clothing [34/118] - Clown
2:07:54 - Litter [27/131]
2:10:32 - Lost Kid [20/40]
2:10:43 - Litter [28-29/131]

Chapter 4: Into the Depths
2:18:53 - Brush Style [11/25] - Leaf
2:19:37 - Litter [30/131]
2:20:16 - Decor [4/100] - Spooky Set
2:28:43 - Brush Style [12/25] - POW
2:29:47 - Lost Kid [21/40]
2:30:01 - Litter [31/131]
2:30:54 - Litter [32/131]
2:35:14 - Achievement Explorer
2:35:15 - Lost Kid [22/40]
2:35:22 - Litter [33/131] + Achievement Trash Mammal
2:37:33 - Clothing [35/118] - Stache
2:42:00 - Decor [5/100] - Couch
2:44:20 - Litter [34/131]
2:45:39 - Deliver Mail [1/12] + Achievement Postal Service
2:47:53 - Litter [35/131]
2:48:47 - Lost Kid [23/40]
2:49:43 - Litter [36/131]
2:57:18 - Brush Style [13/25] - Spray + Achievement Stylist
2:58:25 - Lost Kid [24/40]
2:59:27 - Clothing [36/118] - Spike
2:59:51 - Litter [37/131]
2:59:53 - Litter [38/131]
2:59:57 - Litter [39/131]
3:00:19 - Clothing [37/118] - Bell
3:00:43 - Litter [40/131]
3:01:56 - Clothing [38/118] - Gothy
3:02:25 - Clothing [39/118] - Nice Shirt
3:02:36 - Litter [41/131]
3:08:27 - Litter [42/131]
3:04:21 - Litter [43/131]
3:05:05 - Litter [44/131]
3:05:39 - Brush Style [14/25] - Right Angle
3:06:26 - Clothing [40/118] - Big Fungus
3:07:15 - Clothing [41/118] - Tux
3:07:29 - Litter [45/131]
3:08:11 - Litter [46/131]
3:08:18 - Clothing [42/118] - Spike Helmet
3:13:15 - Achievement Ancient Beast of the Darkness
3:18:53 - Litter [47/131]

Chapter 5: The Source
3:24:11 - Litter [48/131]
3:28:17 - Litter [49/131]
3:29:14 - Clothing [43/118] - Bee
3:30:05 - Litter [50-51/131]
3:30:18 - Clothing [44/118] - Studs
3:30:46 - Litter [52/131]
3:30:50 - Lost Kid [25/40]
3:31:41 - Litter [53/131]
3:31:50 - Clothing [45/118] - Beak
3:32:12 - Clothing [46/118] - Goggles
3:33:52 - Brush Style [15/25] - W
3:34:20 - Clothing [47/118] - Biker Jacket
3:35:09 - Clothing [48/118] - Backwards

Chapters 6: The Wielder Trials
3:46:30 - Achievement Apprenticeship
3:47:50 - Clothing [49/118] - Rex Head
3:48:15 - Clothing [50/118] - Splashpants
3:48:42 - Litter [54/131]
3:49:51 - Deliver Mail [2/12]
3:51:31 - Litter [55-58/131]
3:51:51 - Clothing [51/118] - College
3:52:28 - Clothing [52/118] - Sailor
3:53:00 - Clothing [53/118] - Splash Onesie
3:53:19 - Clothing [54/118] - Rex Bod
3:54:06 - Litter [59/131]
3:54:50 - Litter [60/131]
3:55:02 - Litter [61,62/131]
3:55:28 - Clothing [55/118] - Island
3:56:33 - Clothing [56/118] - Strawhat
3:56:59 - Litter [63/131]
3:57:21 - Clothing [57/118] - Eyepatch
4:00:29 - Litter [64/131]
4:01:16 - Litter [65,66/131] + Achievement Good Samaritan
4:02:27 - Clothing [58/118] - Ahoy
4:03:16 - Brush Style [16/25] - Flames
4:03:51 - Clothing [59/118] - Avast
4:04:45 - Litter [67,68/131]

Chapters 7: The Wielder Trials II
4:11:00 - Achievement More Than Myself
4:11:53 - Litter [69-71/131]
4:12:15 - Clothing [60/118] - Elf + Achievement Clothing Collector
4:12:41 - Litter [72-74/131]
4:13:52 - Deliver Mail [3/12] + Decor [6/100] - Chicory
4:15:58 - Deliver Mail [4/12]
4:17:27 - Decor [7/100] - Camp Set
4:21:08 - Decor [8/100] - Family Portrait
4:22:00 - Lost Kid [26/40]
4:22:08 - Lost Kid [27/40]
4:22:17 - Litter [75/131]
4:22:25 - Litter [76/131]
4:22:28 - Clothing [61/118] - Feather
4:22:36 - Clothing [62/118] - Bard
4:23:03 - Clothing [63/118] - Spellcaster
4:23:16 - Lost Kid [28/40]
4:24:56 - Brush Style [17/25] - Music Note
4:25:19 - Litter [77/131]
4:25:29 - Lost Kid [29/40]
4:26:17 - Clothing [64/118] - Chef
4:26:52 - Clothing [65/118] - Monocle
4:27:09 - Litter [78-80/131]
4:27:48 - Litter [81/131]
4:30:15 - Clothing [66/118] - Dot Dress
4:30:32 - Lost Kid [30/40]
4:31:12 - Clothing [67/118] - Bolt Tee
4:31:43 - Clothing [68/118] - Ski Jacket
4:31:51 - Litter [82/131]
4:32:05 - Lost Kid [31/40]
4:32:20 - Litter [83,84/131]
4:32:25 - Clothing [69/118] - Foxy
4:32:40 - Clothing [70/118] - Gnome
4:33:12 - Brush Style [18/25] - Slash
4:34:41 - Brushflower [1/5]
4:34:57 - Litter [85,86/131]
4:35:24 - Clothing [71/118] - Scientist
4:35:34 - Lost Kid [32/40]
4:35:38 - Litter [87/131]
4:36:10 - Brushflower [2/5]
4:37:18 - Litter [88/131]
4:37:23 - Brush Style [19/25] - Square
4:38:02 - Brushflower [3/5]
4:38:16 - Clothing [72/118] - Stormy
4:39:04 - Brushflower [4/5]
4:39:43 - Brushflower [5/5]
4:39:57 - Clothing [73/118] - Shawl
4:40:44 - Clothing [74/118] - Big Flower
4:40:53 - Litter [89/131]
4:42:19 - Clothing [75/118] - Dorky

Chapters 8: The Wielder Trials III
4:47:03 - Decor [9/100] - Brushflower + Achievement Honored History
4:48:56 - Clothing [76/118] - Square Glasses
4:49:14 - Brush Style [20/25] - Splat
4:50:19 - Decor [10/100] - Studio Set
4:51:34 - Litter [90/131]
4:51:38 - Clothing [77/118] - Nautical
4:55:50 - Clothing [78/118] - Half-Moons
4:56:34 - Clothing [79/118] - Pajamas
4:57:01 - Lost Kid [33/40]
4:57:08 - Litter [91/131]
4:57:34 - Clothing [80/118] - Skate Helmet
4:57:39 - Litter [92,93/131]
4:58:28 - Clothing [81/118] - Hiker
4:58:40 - Lost Kid [34/40]
4:58:45 - Litter [94/131]
4:58:55 - Lost Kid [35/40]
5:01:40 - Achievement Turnabout Squeeze [1/5] - Evidence 1
5:04:23 - Litter [95/131]
5:06:17 - Litter [96-98/131]
5:06:30 - Achievement Turnabout Squeeze [2/5] - Evidence 2
5:08:23 - Litter [99-101/131]
5:08:35 - Litter [102/131]
5:10:17 - Achievement Turnabout Squeeze [3/5] - Evidence 3
5:10:50 - Clothing [82/118] - Top Hat
5:11:54 - Litter [103/131]
5:13:43 - Achievement Turnabout Squeeze [4/5] - Evidence 4
5:14:48 - Achievement Turnabout Squeeze [5/5] - Interrogation
5:20:27 - Clothing [83/118] - Beard
5:20:56 - Litter [104/131]
5:21:28 - Clothing [84/118] - Earmuffs
5:21:41 - Lost Kid [36/40]
5:21:54 - Clothing [85/118] - Puffy Jacket
5:22:26 - Clothing [86/118] - Headscarf
5:23:04 - Clothing [87/118] - Woven
5:23:22 - Lost Kid [37/40]
5:25:21 - Brush Style [21/25] - Mesh
5:27:05 - Litter [105/131]
5:27:22 - Clothing [88/118] - Wintry
5:27:36 - Litter [106/131]
5:31:50 - Brush Style [22/25] - Fine Mesh
5:34:40 - Clothing [89/118] - Fuzzy Jacket
5:35:04 - Litter [107,108/131]
5:37:23 - Clothing [90/118] - Earflaps

Chapters 9: The Wielder Trials IV
5:42:04 - Achievement Standing on the Mountain Top
5:44:17 - Clothing [91/118] - Pilot
5:44:45 - Clothing [92/118] - Headphones
5:44:59 - Lost Kid [38/40]
5:45:08 - Litter [109/131]
5:45:21 - Brush Style [23/25] - Poop
5:45:35 - Litter [110,111/131]
5:45:45 - Clothing [93/118] - Shell Tee
5:49:31 - Litter [112/131]
5:53:49 - Litter [113/131]
5:54:01 - Deliver Mail [5/12] + Decor [11/100] - Gaming TV
5:57:42 - Decor [12/100] - Fan Art
5:59:49 - Lost Kid [39/40]
6:01:56 - Litter [114/131]
6:02:08 - Litter [115/131]
6:02:14 - Lost Kid [40/40] + Achievement Lost and Found
6:02:26 - Litter [116/131]
6:02:32 - Clothing [94/118] - Robo
6:06:03 - Brush Style [24/25] - Custom Colors
6:07:58 - Litter [117/131]
6:08:11 - Clothing [95/118] - Helm
6:09:02 - Clothing [96/118] - Mask
6:09:20 - Litter [118/131]
6:09:42 - Litter [119/131]
6:10:10 - Clothing [97/118] - Horns
6:10:58 - Litter [120,121/131]
6:11:06 - Clothing [98/118] - Pointish Glasses
6:11:47 - Litter [122/131]

Chapter 10: The Brush
6:24:01 - Achievement Respect
6:26:07 - Clothing [99/118] - Crown
6:26:55 - Clothing [100/118] - Mailbag
6:30:16 - Decor [13/100] - Toy Set
6:30:43 - Decor [14/100] - Fancy Set
6:30:47 - Decor [15/100] - Antique Set
7:13:20 - Achievement Something New

Epilogue
7:20:03 - Decor [16/100] - Chicory Flag
7:27:53 - Gelato's Photo [1/5]
7:36:58 - Clothing [101/118] - Custom Hat
7:41:48 - Gelato's Photo [2/5]
7:42:24-8:12:31 - Art Class [3-20/20] + Achievement Graduate
8:12:32 - Decor [17/100] - An Art Degree
8:16:00 - Litter [123/131]
8:16:10 - Clothing [102/118] - Sunny Tee
8:16:58 - Deliver Mail [6/12] + Clothing [103/118] - Sequence
8:18:27 - Clothing [104/118] - Royal
8:19:20 - Deliver Mail [7/12] + Litter [124-126/131]
8:30:14 - Deliver Mail [8/12]
8:31:50 - Litter [127/131]
8:33:02 - Clothing [105/118] - Gorgeous
8:33:36 - Litter [128,129/131]
8:35:23 - Deliver Mail [9/12]
8:37:10 - Decor [18/100] - Classic Painting "Hidden Kitten"
8:37:54 - Decor [19/100] - Classic Painting "Restraint"
8:38:29 - Decor [20/100] - Classic Painting "Cooking Cozy"
8:39:03 - Decor [21/100] - Classic Painting "Fluffy Fluffy Sheep Sheep"
8:39:32 - Decor [22/100] - Classic Painting "The Wizard"
8:39:51 - Decor [23/100] - Classic Painting "Letting Go"
8:40:24 - Decor [24/100] - Classic Painting "A Breezy Field"
8:40:58 - Decor [25/100] - Classic Painting "The Bachelor Party" + Achievement Casual Decorator
8:42:12 - Decor [26/100] - Classic Painting "Portrait of a horse looking back"
8:46:56 - Litter [130/131]
8:48:12 - Litter [131/131] + Achievement Ultimate Samaritan
8:50:05 - Gelato's Photo [3/5]
8:51:49-8:54:19 - Decor [27-55/100] + Achievement Serious Decorator
8:55:34-8:57:23 - Decor [56-74/100]
8:58:09 - Gelato's Photo [4/5]
9:01:44 - Decor [75/100] - Honeysuckle
9:03:01 - Clothing [106/118] - Mascot Bod
9:07:07 - Gelato's Photo [5/5]
9:08:00 - Clothing [107/118] - Tiara
9:08:42 - Achievement Picture Perfect
9:10:44 - Deliver Mail [10/12]
9:12:49 - Deliver Mail [11/12]
9:15:35 - Clothing [108/118] - Antenna
9:18:19-9:20:33 - Decor [76-99/100]
9:22:14 - Deliver Mail [12/12]
9:26:40 - Decor [100/100] - Radish's Art + Achievement Master Decorator
9:27:51 - Oats' Outfit Riddle [1/7] + Clothing [109/118] - Shades
9:28:26 - Oats' Outfit Riddle [2/7] + Clothing [110/118] - Tinted Shades
9:29:01 - Oats' Outfit Riddle [3/7] + Clothing [111/118] - Line Shades
9:29:44 - Oats' Outfit Riddle [4/7] + Clothing [112/118] - Big Shades
9:30:30 - Oats' Outfit Riddle [5/7] + Clothing [113/118] - Rim Shades
9:31:01 - Oats' Outfit Riddle [6/7] + Clothing [114/118] - Aviators
9:31:35 - Oats' Outfit Riddle [7/7] + Clothing [115/118] - Superstar + Achievement Passion for Fashion
9:32:55 - Clothing [116/118] - Delivery + Achievement Such Great Heights
9:34:26 - Clothing [117/118] - Newsie
9:38:51 - Achievement Cartographer
9:38:53 - Brush Style [25/25] - Rainbow + Achievement Style Pro
9:40:41 - Achievement End of an Era
9:41:28 - Clothing [118/118] - Mascot Head + Achievement Clothing Hunter