First Battle[]
This is the battle in which Bourd confrontsLyner alone at Nemo. This battle is impossible to win, given that all the enemies have higher stats than those you're likely to have, and you won't have a Reyvateil either, so Lyner will be knocked out in two turns at most. And while the Tenba Securities accompanying Bourd can indeed by defeated, Bourd himself is scripted to not be possible to reduce his HP to beyond 1, so there's no way of killing him.
Second Battle[]
During this battle, Bourd, given his position as 2nd in command in Tenba, will be accompanied by a trio of Guardsmen, as well as Misha singing Energy Ball in the background. However, Misha will never take any actions during the battle, neither can she be targeted by any attacks, so don't worry about her. Curiously, this is the only battle in the game to feature Berserkr as the background music. Bourd has only two attacks: Stampede, which causes physical damage to a single target, and Earth Crack, which causes large physical damage to all vanguards. Make sure to eliminate the Guardsmen first, as their Super Shot Stored Attack can target Aurica and instantly kill her, but once you have done that, it shouldn't be much problem to take down Bourd as long as you keep your party healthy, which you can easily do by using Krusche's Cure Tablet skill or items like the Heal Cracker.
Third Battle[]
This is the final battle you will have with Bourd, with EXEC_LINKER/. played in the background, and it's exclusive to Misha's route. Bourd got a massive power up following the first battle with him, not only severely increasing all of his stats, but he also gained a new skill: High Voltage, which increases his attack power and adds Thunder-elemental damage properties to both of his skills, changing them into Stampede (Thunder) and Earth Crack (Thunder). Finally, he also got a Lv. 3 Stored Attack called Dread Charge, which if you fail to block even one of the target rings will kill off Misha for sure. All of the above makes Bourd an extremely dangerous enemy, and will make this one of the hardest battles in the game, especially because at this point you still won't have the chance to access to Misha's higher Cosmosphere levels to gain her strongest Song Magics, and because you still can't get the higher-tier equipments and Grathnodes. To counteract this, make sure to use crystals and equipments that increase your Thunder resistance, and try to keep your party at maximum health so Earth Crack in both of its forms doesn't end up wiping out all of your vanguards. Also, make sure to have the max Harmonics level when you finish the battle, as this is the only place from which you can get the Plasma Soul Grathnode Crystal.