During Chapter 8 of Genealogy of the Holy War Coulter appears near Munster accompanied by Altena after Bloom is killed and Connacht is taken by Seliph's forces. He has been ordered by king Travant to take Munster now that Bloom, an ally of the Empire, has been killed. Upon their arrival Altena objects to the attack due to the presence of civilians and tells Coulter and his forces to wait while she tries negotiating with them. Coulter bluntly tells Altena that he has direct orders from Travant to leave no survivors and that her orders cannot override the king's.
Coulter and his squad then flies to and attacks Munster while Altena stays behind and observes from the nearby mountains. Coulter ends up defeated by Seliph's and Leif's forces.
Thracia 776's Chapter 23 depicts the same scenario as his appearance in Genealogy of the Holy War. The scene is slightly condensed which makes him appear a bit less abrasive towards Altena; Altena immediately retreats to speak with Travant about attacking the civilians instead of the conversation being dragged out into an argument.
Either way, Coulter attacks Leif's forces, as Seliph's forces are not present in gameplay here, and ends up either captured or killed.
Coulter has no objections to his orders involving attacking civilians and even says that Altena is "soft" for finding such orders objectionable in such a favorable situation.[1]
...It won't be like this next time. You'll regret this decision!
”
— Coulter when captured and released in Thracia 776
Trivia
Coulter is rather unique in the series, as he is the only boss fought under the same circumstances in two separate games. Interestingly, no attempt was made to make him look visually similar in Thracia 776 to his design in Genealogy of the Holy War, as he uses two completely different generic enemy portraits in both games. His stats and the weapons he uses are also completely different, though his battle and death quotes are largely the same.