This (incomplete) guide focuses on forced battles including "optional" ones that are forced based on choosing a certain response (how was the player to know without reading a guide?) that you may not have to win.
Hugo 1
-Melville's duel vs Guillaume: Hugo has the option to do a quest with Melville's "knights" in Northern Cavern while he has to pass time in Vinay del Zexay, and this duel at the end of the dungeon is unwinnable.
-Leo and Percival when escaping Vinay del Zexay: choosing "No chance" will force Hugo, Sgt Joe, and Lulu into this challenging battle, and you must win or survive 3 turns--the resulting scene will be the same. Choosing "There's no reason to believe you" will avoid battle, and Fubar will come to the rescue.
-duel vs Chris at Karaya Village: if you play Hugo 1 before Chris 1, Hugo can choose "You'll pay dearly!" to attack Chris. You are meant to lose or draw after 3 turns, and winning does not change the dialogue after the duel
Geddoe 1
-generic lizards at Great Hollow: if you do not defeat the lizards within a certain number of turns, the battle ends, but if you get wiped out it's Game Over.
-"Chris" at Great Hollow: losing is the normal route; winning is difficult
-Aila at Karaya Village: this is a pretty easy battle but if you do not defeat Aila's party within 3 turns, the battle ends, and Aila and Queen exchange some words! If you win, Aila's party is kneeling down, weakened by the defeat.
-Borus at Karaya Village: choosing "I have an inkling" will result in a challenging battle vs Borus and 2 Zexen Knights using only Queen and Geddoe. Losing means Game Over!
Hugo 2
-Man in Black at Ancient Highway: choosing "Let's talk to them" OR "Hmm, what's the best way..."+"Hold on now!" will pit your party against the infamous Man in Black. Winning and losing will have their own scenes, and the game will continue.
-Zexen Knights at Great Hollow: choosing "Sergeant, we must join!" will initiate an battle you must win.
Chris 2
-duel with Lucia at Great Hollow: if you play Chris 2 before Hugo 2, Chris can choose "Stop these foolish accusations!" then "So be it" when talking to Lucia to enter a duel. Both winning and losing have their own scenes. Note that if Chris loses, there's a plot-hole, as there is no mention of Harmonia during this scene, and the next scene continues as if Harmonia was the reason they pulled back (because the other dialogue choices lead to the Harmonia news)-- Chris's first line asking about Harmonia seems completely random this way.
-Shiba at Iksay: choose "I'm read to take you on". Losing means Game Over.
-duel with Jimba at Iksay: winning and losing have their own scenes. I'm sure many players have not seen the losing scene for this one!
Geddoe 2
-Franz, Rubi at Le Buque: immediately upon entering Le Buque, the Mantor Trainers will attack (so prepare before entering). You can win or draw after several turns (far more than the normal 3) for different scenes--a draw will result in Geddoe's team complementing the soldiers, but losing will get Game Over.
-Duke's squad and Masked Bishop & Sarah at Flame Champion's Altar: choosing "Sorry, but we have to keep going" OR "We're both in the defense force"+"Sorry, but we have to keep going" will force you in a battle with Duke's team with the chance to go after the Masked Bishiop himself.
1. Against Duke's team, you can win or draw after several rounds (losing gets Game Over). By drawing, Duke will offer to duel, and Geddoe can agree or tell Ace to do it (PICK THIS OPTION!), but regardless of the choice, the Masked Bishop will be done with his inspection and everyone will leave (it plays out the way "That bishop is up to something" ends).
2. If you defeat Duke's team, you will immediately battle the Masked Bishop and Sarah. Note that you will not be given the opportunity to access the menu after defeating Duke's team. Winning and losing have their own scenes.
Hugo 3
-Hugo at Brass Castle when meeting Mua and Hallec: choosing "This time will be different!" will initiate a battle with Leo and Roland. Mua and Hallec will join and you can change the formation. Losing means Game Over.
Chris 3
-Man in Black in Kuput Forest: this battle is winnable but it's ok to lose
-Fight against Man in Black, Masked Bishop, and Sarah: this battle is winnable but it's ok to lose
Geddoe 3
-duel vs Duke at Northern Cavern: you must win this duel in order to continue the game.
General (scenes that can be trigger by any character)
-Rescue Shabon / duel with Guillaume in Vinay del Zexay: Once your character can recruit for Budehuc, if you talk to Nei you will unlock a forced duel with Guillaume if you walk anywhere near the central government building in Vinay del Zexay. Losing means Game Over.