Ever since he had ascended to the throne in 223 BC, Antiochos III was an incredibly active ruler.  The lands under the Arche Seleukeia had been unraveling due to military losses, uprisings, and simple bad luck.  Antiochos inherited these problems; however, the victory over the rebellious usurper Molon, satrap of Media, where Antiochos' very presence itself supposedly caused an entire wing to arrest its attack and surrender before the legal king, seemed to mark an ascension in the fortunes of Seleukeia.  Unfortunately, the defeat at Raphia in 217 BC put a sudden halt to that.  With Aigyptos now militarily revitalized, vigilant and a peace treaty preventing war, Antiochos turned his attention elsewhere: the cities and regions that had broken away from the Seleukid throne.
The first of these was Achaios, who had rebelled and taken the majority of Asia Minor with him only to be defeated by Antiochos in the Siege of Sardis in 213 BC after four years of hard fighting.  Following Achaios was Xerxes of Armenia, who was forced to acknowledge the superiority of the Seleukid throne in the face of overwhelming military might.  After these came the satrapies Parthyaia and Baktria – both of which had broken away decades before.
The appointed Makedonian governor of Parthyaia Andragoras had declared independence from the Seleukid throne and crowned himself king of his province sometime around 250 BC.  Andragoras had persisted until 238 BC when Arsakes, the chieftain of a nomadic, Iranian tribe known as the Parni, deposed him and founded what would be the start of the future Parthian Empire.  It was against the Parni that Antiochos began his anabasis.
The Parni at this time were not a serious military threat to the heart of the Seleukid lands and their centers of power were farther north in Nisa and Dara.  However, they had been conducting raids into adjoining territories from Parthyaia, which resulted in communicative and economic difficulties for those regions.  The small amount of expansion into northern Media that they had pursued after taking control of Parthyaia were now reversed and the raiding put to a stop as Antiochos moved towards and then occupied the city of Hekatompylos after continually winning battle after battle.  The Parni, unable to mount an effective defense, now recognized Seleukid suzerainty.  From here Antiochos traveled through Aria east to the fertile lands of Baktria.
Baktria had broken away from the Seleukids officially at the same time as Andragoras around 250 BC; however, since the 270s, the satrap Diodotos (also known as Theodotos) had been exercising increasing independence, which then increased dramatically during the reign of Antiochos II Theos.  During these years Diodotos began minting coins from the Seleukid mints in the area with his likeness rather than that of the contemporary Seleukid king; yet they still listed the Seleukids as the issuing authority.  It was not until Diodotos died and his son Diodotos II took the reigns of the kingdom did the Baktrians overtly declare independence by naming themselves as the issuing authority on their coins.
The benefits of controlling Baktria were immense.  The land was famed for its fecundity in agriculture and precious metals, but it was also critical as the land connecting the Iranian plateau to India.  Baktria was the crossroads through which trade and influence from surrounding cultures and kingdoms passed.  It is easy to see why reacquiring this kingdom was imperative for Antiochos III; and why the current ruler Euthydemos would not give it up without a fight.  As Antiochos moved forward with his army Euthydemos set out from his capital Baktra with 10,000 cavalry and made camp on the east side of the river Areios; leaving scouts to guard the crossing points on the river.
Antiochos now approached with an advanced force from his main army.  This force was composed of the 2,000 heavy cavalry Hetairoi and Agema that regularly accompanied him into battle, the Argyraspides corps, and small detachments of the light troops and cavalry.  
Upon seeing the Baktrian scouts across the river, Antiochos immediately rushed forth with his 2,000 heavy cavalry to engage the enemy and secure the riverbank.  The resulting melee was vicious and hotly contested until the remainder of Antiochos' cavalry crossed the river and joined in the fighting.  The Baktrian scouts were chased off by the supporting cavalry, but soon Euthydemos arrived with the majority of his force.  The fighting here was even more vicious and Antiochos, according to the historian Polybios, soon distinguished himself as the bravest of all present that day – even suffering a hard blow to his mouth causing him to loose several teeth; yet continuing to fight on.
In the end, the result was a decisive Seleukid victory.  Euthydemos had lost what was probably the overwhelming majority of his heavy cavalry and now retreated to Baktra.  Antiochos gathered the rest of his army, followed quickly behind winning more battles and skirmishes, and laid siege to city.  The siege lasted for two years until peace was achieved via negotiations.  Initially, Antiochos intended to treat Euthydemos as a subject in revolt and as a usurper – the same as he had treated Molon and Achaios.  However, Euthydemos had a truly convincing argument as to why Antiochos should instead accept him as the independent king of Baktria.
Euthydemos' rise to power was not as the heir to the Diodotid line that had originally revolted.  Rather he was instead a deposer of that line; he had not revolted from the Seleukid throne, but removed those who had.  Furthermore, he had protected the eastern territories of the Seleukids from the barbarian nomads, and without him they would be free to to pour into Hellenic lands with the result of barbarization.  Antiochos, tired from the long siege and anxious to continue his campaign, consented and terms were drawn: Euthydemos would resupply the army of and recognize the suzerainty of Antiochos and also gift all his elephants; in return he would be crowned king and rule independently.
With Parthyaia and Baktria pacified, Antiochos traversed the Kaukasia (also known as the Hindu Kush) and down into India.  He renewed links with the Mauryan kingdom and friendship with the current king Sophagesenos.  He received a gift of even more elephants from Sophagesenos (the total now 150) and what even appears to be a tribute.  His anabasis now completed, he returned to Babylon to participate in the New Year festival of April 205 BC.  Before the year was out, however, Antiochos was back on campaign and managed to bring under Seleukid control the entirety of Persian gulf.
From all these achievements, the reconquest of the lost regions of Asia Minor, the humbling of Armenia and the Parni, the victories in Baktria, and the securing of the Persian Gulf, Antiochos received the epithet of Megas – the great.  Perhaps Polybios describes the result of the anabasis best:
This was the extreme limit of the march of Antiochos into the interior, through which he subjected to his rule not only the satraps of the interior but the coastal cities and the dynasts on this side of the Tauros, and in a word he strengthened this kingdom by overawing all his subjects with his daring and energy.  For it was this campaign which made him appear worthy of royalty, not only to the people of Asia but to those in Europe as well (XI 39, 14-16).

Playing the battle:
You begin as Antiochos on the east side of the river with the 2,000 Hetairoi and Agema.  To the far west of the battlefield are the rest of your forces and in front of you are the scouts of Euthydemos.  If you can quickly neutralize them you will free yourself of another worry when the remaining 8,000 cavalry arrive under Euthydemos himself and clear the bank for your other forces to cross the river safely.
Alternatively, you could play as Euthydemos himself riding in the front of the cavalry column in hopes of halting the attempt of Antiochos to reclaim lands that were once his family's.  If you do choose Euthydemos, you start in the extreme north-eastern corner of the map.  Perhaps you could hurry to the battle playing out before you and prevent the Seleukid infantry from ever crossing the river.

Further Note:
It is important and interesting to notice the exact conditions of what suzerainty meant for the Armenians, Parni, and Baktrians.  This was not protectorate status as we know it in the terms of RTW, but rather a form of alliance.  Even then, the alliances were not one of equals, but with a senior and junior partner.  The senior in this case obviously being Antiochos.  In a sense, these would be similar to Rome's alliances with conquered peoples from her wars in the Italian peninsula, and even the Parni and Baktrians had sent troops to fight for Antiochos.
It could be argued that Antiochos should have simply conquered those lands and installed loyal governors and garrisons.  Antiochos would, in fact, later show himself to be an excellent administrator; however, he had neither the time nor the resources to fully re-incorporate the lands.  Many of his soldiers and trusted administrators were busy in Asia Minor and several more would be needed for his renewed efforts in the west.  Furthermore, an independent Baktria could prove to be a powerful buffer state against nomadic raiders (for a comparable example research the Imperium Galliarum of the 3rd Century AD).  Unfortunately, these alliances only lasted as long as Antiochos was alive and became void upon his death; although that had not stopped the Parni and Baktrians from revolting again after hearing the results of Magnesia.