Battle of Mohi might be what you are looking for. It's not a perfect fit but that's the closest I could find.
It was fought on 11th April 1241 between Kingdom of Hungary and Golden Horde. The Battle itself was in fact three sub-battles packed into one, all fought in one day.
Fight at the Sajó bridge - Midnight
Duke Coloman of Slavonia, brother to King Bela IV of Hungary, reached the Sajó bridge to defend it against a possible Mongol attack at midnight as per the intel provided by an escaped Ruthenian slave.
When they reached the river, they found the Mongol vanguard tasked by Batu Khan to capture the bridge and secure the crossing for their main force. The Hungarians caught the Mongols mid-crossing and the battle started. Mongols were caught unaware and their famous horse archers were crippled given the dark and the fact that they were trapped on a narrow bridge, negating their advantage in mobility. The entire vanguard was destroyed and The Hungarians returned to their camp at 0200 HRS after leaving a small detachment to guard the bridge, implying that the fight must have lasted only for half an hour given that The Hungarians were back at their camp within two Hours. Take the time needed to ride back to the camp and to deploy a guard detachment and 30 mins seems like more than reasonable estimate for the duration of battle.
In case you're wondering why would the Duke leave the bridge so weakly held, see my question here.
Main Battle - Morning
At 0400 HRS, Batu Khan attacked The Hungarians at bridge and forced them to retreat. Mongols had now secured their crossing. Retreating Hungarians reached their camp while the Mongols finished the crossing at 0800 HRS.
The survivors from the bridge woke the sleepers at the camp and The Hungarians prepared to meet the Mongols.
The Hungarians outnumbered the Mongols but Subutai was not in the field yet. The Mongols were sore beset within two hours of fighting and as The Hungarians were preparing for another charge to force the Mongols to withdraw, Subutai appeared with his men and attacked The Hungarian rear flank. The Hungarians panicked, sensing that Subutai could encircle them and fled to their fortified encampment. Batu wanted to withdraw for the day given the heavy losses suffered by them but Subutai refused to listen to him and Batu grudgingly consented to resumption of the attack.
Siege of The Hungarian Camp - Afternoon
Situation within The Hungarian camp was becoming dire. The morale was low and they were confined to their camp with Mongols all around them. They tried to sally forth and open a safe passage in the siege lines but they failed everytime. Duke of Slavonia, King's brother, personally tried another sally but he too failed.
Mongols deliberately left a gap in their siege lines, to allow The Hungarians to flee as fleeing soldiers were easier to kill. Many Hungarian soldiers took advantage of the gap, unwary of the trap and were slaughtered down to the last man.
King Bela soon fled with his brother as well but the Duke took so grievous injuries that he died soon after. The battle was over and The Hungarian force was virtually wiped out.
Conclusion
- Three "fights" were fought in the battle on the same day.
- The results were mixed. The Hungarians won the first one but Mongols won the other two. Overall, it was a decisive Mongol victory.
- The fights were between the same two belligerents, not four different belligerents as with Robert Baratheon.
- There were no three distinct battles but that is the case with Summerhall as well, three fights of the same battle were fought there.
