Hive Fleet Behemoth
Hive Fleet Behemoth was the first Tyranid Hive Fleet to enter the galaxy. It was destroyed during the First Tyrannic War of 745-746.M41. The discovery of the Tyranids, as heralded by Behemoth, was one of the first major events in the Time of Ending.
For nearly a decade prior to their discovery, the Explorator Fleets were aware that something was happening out in the Eastern Fringe, as worlds which had previously been confirmed to support life had been reduced to Dead Worlds, even to a microscopic scale. Inquisitor Kryptman of the Ordo Xenos was dispatched to investigate. When he reached the Explorator Base on the planet Tyran, he discovered a lifeless rock, but a single data-record was left detailing what happened, leading to the current designation of the Tyranids as such (Tyran ID = 'Tyranid/s'). Kryptman then branded them as xenos horrificus, an alien form of life so destructive that extinction was the only option. Analyzing the path of known Tyranid attacks and extrapolating a future course, he discovered that they were heading straight for Ultramar.
While moving towards Ultramar, the Hive Fleet ate a moon-sized chunk of biomass the Imperium held for 9000 years at Occulus, fought the Star Krumpa Freeboota Orks who had been plaguing this part of the galaxy for years; finding their first serious fight (noted by the boyz involved as a particularly great fight) but eating most of the Orks in the end, had two scout tendrils dodge around Trazyn's dynasty at Solemnance, and annihilated the Death Shadows Chaos Space Marines at Sybari.
Upon learning of this, the Imperium of Man suspended the Damocles Crusade currently underway against the Tau Empire, in order to re-allocate resources and because the High Lords of Terra had determined that the Tau would serve as a nice buffer/buffet between them and the new threat.
Marneus Calgar, the Chapter Master of the Ultramarines, took most of the Chapter to the Ultramar world of Prandium. Despite this concentration of force, the Tyranids were able to overwhelm the Ultramarines and force them to abandon Prandium. Calgar spent a week fasting and declared that the Ultramarines had suffered the sin of pride by allowing themselves to become complacent (bear in mind this was years before our spiritual liege was working at Games Workshop).
Falling back to Macragge, the Ultramarines fortified their chapter homeworld, but the Tyranids responded by unleashing the powerful and specialized variant of Hive Tyrant, the Swarmlord. Despite the best efforts of his Honour Guard (including the
force feeding sacrifice of their commander), Calgar was so grievously wounded that he lost both his arms and legs, one eye, and his stomach, and had to retreat to orbit, leaving the northern polar fortress with only the First Company to defend it.
Fortunately, Imperial Navy reinforcements from Segmentum Tempestus (yes, the Tyranids were so bad they needed reinforcements from another Segmentum) finally arrived. The battle only turned in the Imperium's favor when the Emperor-class Battleship Dominus Astra detonated its warp-drive, dragging most of Hive Fleet Behemoth into the Warp and letting them meet the Chaos Gods*. Returning to Macragge, the Ultramarines Third Company scoured the northern fortress, where they discovered First Captain Saul Invictus and the entire First Company had been killed to a man. Only one member of the First Company, Battle-Brother Altarion, had survived the battle, and he was so messed up that he had to be put into a Dreadnought, which of course invites philosophical debate on whether he actually died or not, but that's for another day.
[*] We can only hope this doesn't come back to bite us later.
While the Imperium had achieved a victory on the battlefield, the cost of Hive Fleet Behemoth was severe. An entire world of Ultramar was lost and the Ultramarines First Company with it. Captain Severus Agemman of the Second Company was promoted to First Captain of the Ultramarines, while Veteran Sergeant Cato Sicarius was promoted to Captain of the Second Company. The losses the Ultramarines suffered were so great that Dante sent several companies of the Blood Angels to help the Ultramarines purge the remaining Tyranids from Ultramar.
Nearly a century later, the Ultramarines had still not fully recovered from the losses Hive Fleet Behemoth had inflicted, but by that point Macragge was cleansed of Tyranids. Several ships of Behemoth survived, but without the coordination of the Hive Mind they broke apart into smaller Hive Fleets. The Swarmlord was officially listed as destroyed in action, but its corpse was never located.
Despite all their losses the Ultramarines believed that they had crushed the Xenos threat and another enemy of the Emperor was no more. Such hopes came to haunt them when two and a half centuries later, Hive Fleet Kraken assaulted the Imperium's borders…
Hive Fleet Gorgon
Gorgon is one of the Behemoth splinter fleets that survived and nommed its way to the Eastern Fringe and the Tau Empire. Unlike other hive fleets, this one was relatively small, but was capable of fast adaptation to new weapons and tactics to evolve to overcome resistance to the Swarm. To fight against the Tau, knowing their cheesy plasma weaponry deals too much damage for their large biomorphs to handle, it decided to zergling rush into the fire warriors' firing line by shitting out expendable hormagaunts.
The Tau are also known for battlefield adaptation and evolving technology; they responded by switching to older or newer weapons when dealing with Gorgon's rapid adaptation. The Tau found that Hive Fleet Gorgon lacked more complicated Synaptic creatures (which required more time to modify), and declared an anti-Synaptic hunt that only Tau with their weeaboo battlesuits, sneaky kroots, and swarms of cheap aircraft could perform, so huge swarms of the specialized gaunts Gorgon relied upon went feral and were easily dealt with. To add insult to injury, Imperial Guard reinforcements lost in the Warp earlier during the Damocles Crusade arrived and allied with the Tau to fight the more immediate threat of the Tyranids, further diversifying the range of ordnance to counter Gorgon adaptation.
Court of the Nephilim King
Another splinter fleet, these guys were so small at first that they evaded the sensors used by the ultramarines and escaped before going dormant for a while. Centuries later, they reawekened and attacked the nearby unsuspecting worlds, gaining enough biomass to become a threat. They earned the name "court of the Nephilim King" when they attacked a homeworld of Imperial Knights, who decided to give them fancy, kingdom-inspired names because they are pretentious bastards like that. Even though the nids were defeated, the knights still were impressed by their ferocity.