I've paired up with +ZakuranHD to link you to a comprehensive set of YouTube videos covering The Legend of Heroes: Trails in the Sky SC.

+midoshiro
This is pretty much a full video walkthrough of the Traditional Chinese version of The Legend of Heroes: Trails in the Sky SC. Edits were made to the videos to removing the boooooring parts of the game (travelling, dungeon crawling, and regular monster fights).
Playlist
+ZakuranHD
All the boss fights for the English version of The Legend of Heroes: Trails in the Sky SC hard mode, in addition to the opening part of the Prologue chapter.
Playlist

Prologue Chapter

SC starts immediately after the events of FC. Estelle awakens the morning after and begins her search for Joshua -- starting from the Bright house. There, she is convinced to enroll in special Bracer training.

+midoshiro
Chapter 0, Part 1 of 4 Part 1 of 4
21:00
Chapter 0, Part 2 of 4 Part 2 of 4
13:06
Chapter 0, Part 3 of 4 Part 3 of 4
8:35
Chapter 0, Part 4 of 4 Part 4 of 4
10:54
+ZakuranHD
Prelude Prelude
6:19
Opening Opening
6:58
Kurt Kurt
5:12
Jaegar Jaegar
5:42
Female Jaegar Female Jaegar
5:38
Jaegar 2 Jaegar 2
15:45

Chapter 1

After completing special Bracer training, Estelle and Anelace head to Grancel where they meet Scherazard Harvey and Agate Crosner. They split into two pairs to help out the other Bracer guilds and to investigate the Ouroboros.

Estelle heads to Ruan and begins investigating rumours of a white shadow coming out at night. Her investigation leads her to the Underground Ruins at the Old Schoolhouse behind Jenis Royal School where she meets Legion X, Blblanc.

+midoshiro
Chapter 1, Part 1 of 6 Part 1 of 6
20:37
Chapter 1, Part 2 of 6 Part 2 of 6
27:19
Chapter 1, Part 3 of 6 Part 3 of 6
25:39
Chapter 1, Part 4 of 6 Part 4 of 6
20:13
Chapter 1, Part 5 of 6 Part 5 of 6
24:07
Chapter 1, Part 6 of 6 Part 6 of 6
20:24
+ZakuranHD
Raven Gang Raven Gang
8:34
Highway Monster 1 - Cobalt Sabers Highway Monster 1 - Cobalt Sabers
5:50
Highway Monster 2 - Mercury Vipers Highway Monster 2 - Mercury Vipers
4:36
Highway Monster 3 - Ash Sabers Highway Monster 3 - Ash Sabers
2:26
Highway Monster 4 - Hapilsag Highway Monster 4 - Hapilsag
3:27
Storm Bringer Storm Bringer
18:34

Chapter 2

Having solved the mystery of the white shadow in Ruan, Estelle makes her way onward to Zeiss where she is greeted by an earthquake, unusual for the Liberl Kingdom. Kirika, of the Zeiss Bracer Guild, suspects the Ouroboros may have something to do with the recent earthquakes and asks Estelle to investigate.

With the help of Professor Russel's seismographs, the Capel supercomputer calculates the source of the earthquakes to be at The Fountainhead behind Elmo Village. There, Estelle meets Legion VIII, Walter, the Lanky Wolf.

+midoshiro
Chapter 2, Part 1 of 6 Part 1 of 6
25:33
Chapter 2, Part 2 of 6 Part 2 of 6
28:34
Chapter 2, Part 3 of 6 Part 3 of 6
33:10
Chapter 2, Part 4 of 6 Part 4 of 6
28:23
Chapter 2, Part 5 of 6 Part 5 of 6
26:44
Chapter 2, Part 6 of 6 Part 6 of 6
29:25
+ZakuranHD
Highway Monster 5 - Whale Frog Highway Monster 5 - Whale Frog
4:31
Lieutenant Colonel Cid Lieutenant Colonel Cid
11:41
Highway Monster 6 - Mantraps Highway Monster 6 - Mantraps
3:39
Highway Monster 7 - Ya-Kah Highway Monster 7 - Ya-Kah
2:43
Highway Monster 8 - Bloody Saber Highway Monster 8 - Bloody Saber
4:47
Abyss Worms Abyss Worms
18:45

Chapter 3

Having solved the earthquakes in Zeiss, Estelle and team now find their way to Grancel, the capital of the Liberl Kingdom. Here, after finding a lost child (Renne), the team helps the military investigate a series of threatening letters being circulated.

+midoshiro
Chapter 3, Part 1 of 6 Part 1 of 6
34:33
Chapter 3, Part 2 of 6 Part 2 of 6
24:24
Chapter 3, Part 3 of 6 Part 3 of 6
32:43
Chapter 3, Part 4 of 6 Part 4 of 6
34:00
Chapter 3, Part 5 of 6 Part 5 of 6
33:12
Chapter 3, Part 6 of 6 Part 6 of 6
33:50
+ZakuranHD
Highway Monster 9 - Cronociders Highway Monster 9 - Cronociders
5:18
Highway Monster 10 - Mad Trees Highway Monster 10 - Mad Trees
7:00
Highway Monster 11 - Gundoll Highway Monster 11 - Gundoll
6:40
Special Ops Soldiers Special Ops Soldiers
3:25
Orgueille Orgueille
17:27
Kanone Amalthea Kanone Amalthea
8:00
Highway Monster 12 - Flame Velgr Highway Monster 12 - Flame Velgr
7:48

Chapter 4

Estelle and team make their way to Rolent, which has somehow been enveloped in a thick fog. Estelle tracks down Mistwald as being the source of the fog and heads over to investigate. There, she finds the next member of the Ouroboros.

+midoshiro
Chapter 4, Part 1 of 6 Part 1 of 6
31:54
Chapter 4, Part 2 of 6 Part 2 of 6
35:58
Chapter 4, Part 3 of 6 Part 3 of 6
34:51
Chapter 4, Part 4 of 6 Part 4 of 6
35:42
Chapter 4, Part 5 of 6 Part 5 of 6
34:59
Chapter 4, Part 6 of 6 Part 6 of 6
30:02
+ZakuranHD
Joshua vs Mueller Joshua vs Mueller
12:49
Highway Monster 13 - Wisdom Highway Monster 13 - Wisdom
4:42
Highway Monster 14 - Giantfoots Highway Monster 14 - Giantfoots
4:53
Highway Monster 15 - Thunder Quakes Highway Monster 15 - Thunder Quakes
5:50
Highway Monster 16 - Death Specular Highway Monster 16 - Death Specular
6:01
Jubokko & Zaqqum Jubokko & Zaqqum
9:10

Chapter 5

TODO: summary

+midoshiro
Chapter 5, Part 1 of 4 Part 1 of 4
34:47
Chapter 5, Part 2 of 4 Part 2 of 4
34:11
Chapter 5, Part 3 of 4 Part 3 of 4
34:20
Chapter 5, Part 4 of 4 Part 4 of 4
32:36
+ZakuranHD
Highway Monster 17 - Blade Fang Highway Monster 17 - Blade Fang
5:15
Highway Monster 18 - Ghost Epitaph Highway Monster 18 - Ghost Epitaph
5:47
Highway Monster 19 - Octobone Highway Monster 19 - Octobone
4:11
Highway Monster 20 - Fate Spinner Highway Monster 20 - Fate Spinner
3:07
Ragnard Ragnard
22:32

Chapter 6

TODO: summary

+midoshiro
Chapter 6, Part 1 of 4 Part 1 of 4
32:32
Chapter 6, Part 2 of 4 Part 2 of 4
34:16
Chapter 6, Part 3 of 4 Part 3 of 4
33:05
Chapter 6, Part 4 of 4 Part 4 of 4
9:56
+ZakuranHD
Bracer Laboratory Fights Bracer Laboratory Fights
18:01
Doppelgangers Doppelgangers
8:01
Enhanced Jaegers Enhanced Jaegers
7:46
The Miracle in the Sky The Miracle in the Sky
22:36

Chapter 7

TODO: summary

+midoshiro
Chapter 7, Part 1 of 5 Part 1 of 5
30:01
Chapter 7, Part 2 of 5 Part 2 of 5
31:45
Chapter 7, Part 3 of 5 Part 3 of 5
37:16
Chapter 7, Part 4 of 5 Part 4 of 5
31:01
Chapter 7, Part 5 of 5 Part 5 of 5
13:20
+ZakuranHD
Enforcer X: Bleublanc Enforcer X: Bleublanc
10:20
Enforcer VIII: Walter Enforcer VIII: Walter
10:58
Enforcer VI: Luciola Enforcer VI: Luciola
8:26
Enforcer XV: Renne Enforcer XV: Renne
8:27
Pater-Mater Pater-Mater
8:35

Chapter 8

TODO: summary

+midoshiro
Chapter 8, Part 1 of ? Part 1 of ?
30:26
Chapter 8, Part 2 of ? Part 2 of ?
36:10
Chapter 8, Part 3 of ? Part 3 of ?
36:38
Chapter 8, Part 4 of ? Part 4 of ?
37:03
Chapter 8, Part 5 of ? Part 5 of ?
34:04