I'm pretty certain the Armenian Kingdom of Cilicia is involved... the place names seem to be part of that Kingdom. I'm having some trouble determining opponents... I think likely the Turks, but google doesn't give solid info tying the dates to battles very well in this case, so it could also be against the Byzantines or even the Crusaders, although I think the later to be less likely. I'm even leaning a towards the Byzantines rather than the Turks as an Armenian leader was imprisoned by Byzantium about that time (as a rebel prince, I believe).
Here's my best guess, then... and google is sketchy on the fine points, so it's only a guess based on slim research...
Armenian Kingdom of Cilicia vrs the Byzantines with the Armenian side the victors (I judge them victorious based on the fact that they were a going concern as a kingdom will after the time of these battles).
Very good deduction.
Battle of Anazarbus: From 1102-1103 onwards, Toros I assisted the crusaders to neutralize the attacks of Byzantine at Edessa and Antiochia. Later he allied with Prince Tancrède of Antiochia and began himself to fight against Byzantium, conquering the important city of Anazarba. (info from Armenica.org I believe)
Battle of Marash: The hatred and the hostility of the Turks towards New Armenia was bought with the gold that the Byzantine court paid to the Turks, since the gaze of Byzantine still was fixed on Cilicia and even the Antiochia duchy. The brother of Levon I, Stephan, in 1135 took the city of Marash which was in Turkish hands.
Battle of Mamistra: Emperor Manuel (1143-1180), of the Comnenos dynasty, then sent an army of 12,000 men, under the leadership of Andronikos Comnenos, against the Armenians and, with the help of some of the Armenian noble families who were at war with the Rouben-Bagratouni family, was able to drive back Toros II and his forces. Toros took position in the strong fortress of Mamistra and was surrounded of the Byzantine forces. As it was a surprise attack, and the Armenians had not had the opportunity to gather necessary provisions for a siege, their situation was critical. The Armenian forces left the fortress at night and engaged with the Byzantine army which was several times stronger then them. A harsh battle began, which ended in a glorious Armenian victory. Several of the enemy officers were captured and were later exchanged for a large ransom.
When Emperor Manuel was informed of the defeat, he convinced sultan Massoud, the lord of Konya, to attack New Armenia, but Toros twice fought back the enemy forces. Then Massoud allied himself with Renauld de Chatillon, the prince of Antiochia, who was quarrelling with Toros over the fortress of Gastin in the Amanus Mountains, and asked that Antiochia declare war on New Armenia. Nonetheless, change of sides also ended with an Armenian victory near the Gulf of Eskanderun.
The battle of Mamistra was by fa the most major of them. You know, this make me want to do an Armenian campaign and post about it.