The incident of the Virata War has been narrated in the Goharana Parva of the Virata Parva of the Mahabharata. A small background - The Kaurava army invades the Matsya Kingdom from the north and steals their cattle (Chapter 35). Uttara, the son of King Virata, who is encouraged by the chief cowherd to face the army, takes Arjuna, dressed as Brihannala, as his charioteer. They recover the weapons of the Pandavas, Arjuna loses his eunuch garb (Chapter 45) and sets out with Uttara as his charioteer.
Arjuna first goes behind Duryodhana’s army and frees the cows.
All the Kauravas too reach there and Arjuna opts to engage Karna, but is intercepted by some warriors (Karna’s brother Sangramajit, etc) and the battle ensues.
1. Vikarna (One of the 100 brothers) vs. Arjuna:
Then cutting Vikarna's bow furnished with a tough string and horns overlaid with gold, Arjuna cut off his flagstaff. And Vikarna, beholding his flagstaff cut off, speedily took to flight
2. Karna vs. Arjuna:
And that grinder of foes pierced Karna's arms and thighs and head and forehead and neck and other principal parts of his body with whetted shafts endued with the impetuosity of the thunderbolt and shot from the Gandiva in battle. And mangled and afflicted by the arrows shot by Partha the son of Pandu, Vikartana's son (Karna) quitted the van of battle, and quickly took to flight, like one elephant vanquished by another. (Chapter 54)
Arjuna then directs Uttara to go towards Kripacharya while destroying the formation of the army and killing miscellaneous warriors on the way.
3. Arjuna vs. Kripacharya:
And those illustrious bulls among men, taking Kripa with them who had been deprived of his car, led him away from the vicinity of Dhananiaya, the son of Kunti. (Chapter 57)
4. Drona vs. Arjuna
Partha gave Drona an opportunity to leave the field. And thereupon the latter, wounded in that terrible encounter, and his mail and banner gone sped away by the aid of swift horses. (Chapter 58)
5. Ashwatthama vs. Arjuna
And as Aswatthaman's arrows, in consequence of his ceaseless discharge in that conflict, were quickly exhausted, it was for this that Arjuna prevailed over his adversary. (Chapter 59)
6. Karna vs. Arjuna II
Karna's vision was obscured and his senses left him. And regaining consciousness, he felt a great pain, and leaving the combat fled in a northernly direction.
Arjuna then proceeds towards Bhishma but is intercepted by Duhshasana, Vikarna, Duhsaha and Vivimsati, the sons of Dhritarashtra.
7. Sons of Dhritarashtra vs. Arjuna
And afflicted by the arrows of Partha. Dussasana fled, leaving the combat...And pierced by Arjuna, he (Vikarna) fell down from his car. ... both those sons of Dhritarashtra (Duhsaha and Vivimsati), deprived of their steeds and their bodies mangled were taken away by the warrior behind them. (Chapter 61)
After this all the Maharathis of the Kuru army collectively began to pursue Arjuna who effectively countered them. After this, the formation made by Kripacharya, Karna and Drona was demolished by Arjuna’s Aindrastra. Seeing these warriors being defeated, Bhishma decided to face Arjuna himself. (This seems like they did fight with Arjuna but the word ‘all’ seems more like a hyperbole in this context. The entire Kuru army literally came later when Arjuna used the Sammohana Astra)
8. Bhishma vs. Arjuna
Ganga's son of mighty arms and irresistible in battle, stood for a long time leaning on the pole of his car. And beholding him deprived of consciousness the driver of his car-steeds, calling to mind the instructions about protecting the warriors when in a swoon, led him away for safety.
9. Duryodhana (and Vikarna) vs. Arjuna
Vikarna having broken and fled along with the supporters of the king's car, the other warriors, smitten with the arrows shot from the Gandiva, fled from the field in panic. And beholding the elephant slain by Partha, and all the other warriors running away, Duryodhana, the foremost of the Kurus, turning away his car precipitately fled in that direction where Partha was not.
10. The use of the Sammohana
Having been insulted, Duryodhana returns to face Arjuna, accompanied by Karna. Seeing them even Bhishma, Drona, Kripacharya Vivimsati ans Duhshasana begin attacking Arjuna, to protect Duryodhana. In effect it is Arjuna versus the entire Kuru army. It is at this point that he uses the Sammohana Astra:
the wielder of the Gandiva who was capable of enduring all foes, evolved another irresistible weapon obtained from Indra, called Sanmohana. And entirely covering the cardinal and other directions with sharp and keen-edged arrows furnished with beautiful feathers, that mighty hero stupefied their senses with the twang of the Gandiva. And once more, taking up with both his hands that large conch of loud blare, Partha, that slayer of foes, blew it with force and filled the cardinal and other points, the whole earth, and sky, with that noise. And those foremost of the Kuru heroes were all deprived of their sense by the sound of that conch blown by Partha. And all of them stood still, their bows, from which they were never separated, dropping down from their hands. And when the Kuru army became insensible. (Chapter 65, 66 as per Gitapress)
11. Bhishma’s intervention
Arjuna knew that only Bhishma was unaffected by the weapon. When the army regains their senses, Duryodhana requests Bhishma to engage with Arjuna and not let him get away to which Bhishma says these wise words:
Where had been this sense of thine, and where had been thy prowess too, when thou hadst been in a state of unconsciousness renouncing thy arrows and handsome bow? Vibhatsu is not addicted to the commission of atrocious deeds; nor is his soul inclined to sin. He renounceth not his principles even for the sake of the three worlds. It is for this only that all of us have not been slain in this battle. O thou foremost of Kuru heroes, go back to the city of the Kurus, and let Partha also go away, having conquered the kine. Do thou never foolishly throw away thy own good. Indeed, that which leadeth to one's welfare ought to be accomplished.(Chapter 65, 66 as per Gitapress)
Duryodhana considering Bhishma’s words to be of his benefit, abandons the will to continue on. Arjuna thereafter does Namaskaram to all the elder Kuru warriors and returns to Virata victorious:
And the Kauravas were unable to confront Arjuna while after routing (defeating) the foe he proceeded towards the city of Virata, like an elephant with rent temples.
(Note:- I have tried to cut out unimportant parts which can be read from the links on the website. Tried to make it as short as possible but has turned out still too long)