Most enemy stats (apart from some bosses) are slighlty randomized at the start of a chapter (including MOV) right after the RNG is reseted, and since there are 64 different seeds, it means there are only 64 different sets of stats possible. Some strategies require some specific stats to work (like low enough to be OHKO or an extra point of MOV).
Chapter 1
The second soldier must have 6 MOV and 3 or less LUK, the boss must have 1 or less LUK (2 seeds possible)
With my Turn 1 formation, if the first soldier is still alive and the second one happens to have 6 MOV, the later will attack Leif in close combat for some reason (usually he will always attack from a distance, thus wasting some time with the Light Brand animation). The boss must be killed with a critical hit, and Leif must get a MGC, MOV and Movement Star proc, which is only possible with the 5% crit string, which is why Leif must have 5 SKL and the boss must have 1 LUK at most (else the attack will have less than a 5% critical rate).
Chapter 2
The boss must have the minimum amount of HP and MGC, as well as not too much Avoid (1 seed possible)
There are 6 seeds with a 31 HP/1 MGC boss, but out of them, only one works with the 66% hit string.
Chapter 2x
While this chapter isn't mandatory, not visiting it would actually take a lot of time since I would have to wait several turns in chapter 2 for the pirates to destroy a house (they are really slow at doing it). So it's more efficient to do it to get some MOV level-ups, as well as killing Shiva in the way to prevent him from spawning in chapter 7.
Chapter 3
One specific kid must be saved to get the Warp Staff at the end of chapter 7. This is the only place where I can kill Tanya so that I can get Dagdar instead of her at the end of chapter 8, and he is far more useful than her (high stats, Movement Stars). The soldier near Dagdar didn't attack him on Turn 2 because he would have dealt any damage.
Chapter 4
The Light Brand must be in the closest chest, the second soldier must have enough BLD to capture Macha (2 seeds possible)
First of a serie of 4 Escape Maps. Nobody can keep up with Leif's mobility, so nobody is gonna escape appart from Lara since she will be useful later on. She has 3 BLD so Leif must have at least 6 BLD in order to carry her without any movement penalty. The only reason I must get back the Light Brand is because of the chapter 10 boss.
Chapter 5
The exit of the map will not open until you open the door to the arena. Leif must face a precarious enemy phase while still getting the usual MOV level-up.
Chapter 6
I purchased 6 Door Keys (precious in this game) as that's just the amount I will need.
Chapter 7
If Shiva was still alive, he and his men would have spawn in this map and block my path.
Chapter 8
Safiya got the Life Ring from chapter 1 to help manage her Fatigue (else she can't reach 25 HP in time). Since I previously unequipped Marty, he will walk to to shop to try to buy a weapon, thus getting closer to Halvan who is then able to recruit him.
Chapter 9
I left behind my 3 non Movement Stars units + Callion who is the least useful of the remaining ones. Robert rescued Leif and then Escapes with him so that Leif kept his Movement Stars ability at the start of the next chapter.
Chapter 10
This boss is a pain to kill and the reason why I had to get back the Light Brand. His avoid is so high that I can't get (in a reasonnable amount of time) an RNs string with a crit + MOV + Movement Stars proc, which is why I had to kill an extra enemy in chapter 8 (I need 19 MOV for chapter 13).
Chapter 11
This boss is unkillable and will leave on the next enemy phase after you tried to hit him, so Ronan was sent and then immediatly throw his weapon to force the armor to capture him without a fight.
Chapter 12
Mareeta appears (and is automatically recruited) at the end of Turn 1 and is kinda important to recruit a character later on (both of them being Movements Stars characters with combat abilities), so it was the perfect time to repair the broken Warp Staff thanks to Safiya peronnal Staff. Salem may use his Sleep Staff during the enemy phase, and he was manipulated to not do so.
Chapter 12x
Some enemies may or may not move during the enemy phase, based only on the RNG.
Chapter 13
With 19 MOV, Leif has just enough mobility to Escape on Turn 1 with Lara, thus dodging a very long enemy phase. Robert helped to give Lara to Leif, and everyone else was a non Movement Stars unit.
Chapter 14
Some key units must not have an extra point of movement, the enemy turn order must be favorable to reduce the length of the enemy phase (very few number of seeds possible)
There can't be more than 50 enemy units at the same time in a chapter, so it's actually beneficial to not kill enemies in order to prevent reinforcements to appear. The Dracoknights at the end each have a 70% to move each turn, and there is no quick RNs string available to have only one of them moving, so I went for 2 instead.
Chapter 15
Since I don't need to recruit Schroff, I can go directly to the right arrow and I don't have to visit the church in the middle (which would cost 1 Warp usage).
Chapter 16A
For the same reason, I can warp Leif direclty to boss (after dancing him to recover his Movement Stars ability).
Chapter 17A
Spent one extra turn in order to recruit Sarah (I had to repair my Warp Staff anyway), but she is pretty much mandatory as the fastest to recruit Movement Stars unit who can use the Rescue Staff in chapter 19. I got a Warp Staff and a Rescue Staff from the houses.
Chapter 18
Warp Leif, kill the boss, Seize. Leif must have 16 STR to kill him in one turn.
Chapter 19
I have just enough units to group gather the south units into 3 groups, which allows me to rescue them with the 3 uses of the Rescue Staff from chapter 17A. I was very short on Movement Stars unit (and I want Lara to keep her ability for the furst turn of the next chapter) but I managed to do it by playing around the Rescue/Transfer mechanics.
Chapter 20
The left side Armor must have 6 MOV to be able to open the door one Turn 1 (7 seeds possible)
It's faster here to prevent the reinforcements from appearing by blocking the squares where they spawn than using a strategy similar to chapter 14. I put 2 Armors to sleep to help me in this task (since their squares are close to the boss and his bodyguards, they are very inconveninent to block with my own units), while the third and last use was to prevent the Armors in the northeast cell to waste animation time every turn. The boss can't be killed in the first three turns, but I am not in a hurry because only some reinforcements from Turn 12 onward can be prevented by killing him. I had a very nice RNs string to get a BLD level-up for Safiya (she needed to repair the Warp Staff at some point in this chapter).
Chapter 21
Leif can't be warped next to the boss so Dean is sent first instead.
Chapter 21x
I must deploy 8 units but I only had 5 non Movement Stars units and I wanted everyone but Leif to keep their Movement Stars ability. I found a way to do so with a Rescue/Transfer trick similar to chapter 19, but it was only possible thanks to Safiya getting this extra point of BLD to carry Sarah.
Chapter 22
Same as chapter 21.
Chapter 23
Warp Leif, kill boss, Seize.
Chapter 24
I recruited Galzus with Mareeta as he can kill the boss instead of Leif and is very useful for the Final chapter (both for his stats and for his weapons). It also allows me to not have Lara in the same group than Leif, which would have made my Final chapter strategy impossible.
Final chapter
The 2 Armors in the top left room must have 7 STR (1 seed possible)
I had 15 units to work with, including 7 without a Movement Stars ability on Turn 1 (the 5 usuals + Leif + Cyas), which lead to 3 groups of 3 people and 3 groups of 2. To clear each room on Turn 1, I needed to have 4 actions per group (open the door, kill 2 enemies, place an unit in the center of the room), which wasn't possible with my army (I would need 1 more guy to have his Movement Stars ability basically).
However I came with an alternative strategy which made good use of the excess of actions I can get from Lara's group thanks to her Dance + Movement Stars, putting her in Cyas' group so that he could solo clear the room and Warp the third guy (Dagdar) to an otherwise unclearable room. After being warped, any Movement Stars unit can kill the two enemies and occupy the center with his two actions. The top left room was chosen for this because the guys here can be so weak (11 Atk both) that they won't try to attack him on enemy phase, saving some time. This led to the least reliable round of combat of the whole TAS, with dodging a 83% attack (Berserk Sword) followed by a 8% Hit 7% Crit, to then proc a 5% Movement Stars (so a 1 in 21000 chance of success...).
I don't think you can go faster with any less units. My final army consists mainly of automatically recruited units, with the only ones who cost some sort of time to recruit/keep being Safiya/Lara (mandatory), Dagdar (instead of Tanya), Mareeta (needed for Galzus, I must repair the Warp Staff at some point anyway), Sarah (mandatory for chapter 19) and Galzus (I pretty much can't kill the final boss without him or his weapons).
In retrospect, it might be possible to kill the chapter 10 boss with a crit and still get a MOV level-up and a Movement Stars proc (so I wouldn't need the extra level-up against the Warrior in chapter 8), but I would need to have EVEN MORE SKL, which would be tedious given the other low % stats I must get every time.
Other than that, better micro management (I think my keys management could have been slighlty better for example), though it would still be limited by the time you have to wait for seeds management.