Hunting and killing the Alien Queen is a great honor for the Predators and many have died doing so. It is even more useful to capture a live Queen and use her as a breeder to obtain Alien eggs. Here is a list of notable Predator vs. Alien Queen fights, including some attempts to capture her alive.
Young Predators vs. Escaped Queen
In Alien vs. Predator: War, Topknot's clan had captured a live Alien Queen and bought her on board their ship. When Machiko Noguchi, a human living and hunting together with the Predators heard that the Predators had started hunting humans, she decided the betray them and release the captured Queen. The freed Queen immediately went to work on lightly armed young blood Predators, who were quickly overwhelmed. Although the Queen was outnumbered, she had the element of surprise and the young Yautja could only find pickaxes to use against her. The young bloods were quickly killed off and the Queen soon escaped to the surface of planet Bunda. This is also one of the few cases of an Alien Queen winning the fight against Predators.
Vega 4 Predator vs. Orion Nebula Queen
In the first Alien vs. Predator video game on the SNES, a lone Predator traveled from VEGA 4 to the Orion Nebula, presumably to Xenomorph Prime. After taking down several different Xenomorph types, including the Snake Alien, he encountered the Alien Queen as the final boss. The Queen was actually not so large by Xenomorph standards, but bulky and agile. After some jumping and punching, the Vega 4 Predator was able to take down the Queen. It was stated that "all races in the galaxy owned the Predator a great debt" by killing the Queen. The fight, like the game itself, was somewhat underwhelming.
Three World War Predators vs. Alien Queen
Ten years after the events on Ryushi in the first Alien vs. Predator comic, Machiko Noguchi was again involved with the Predators trying to capture a live Alien Queen. The Queen was probably a decadent of the Xenomorphs on Ryushi and had emerged to be their leader. This time, the Predators had help from Colonial Marines. The team-up had happened to fight against the Killer Predator clan, a ruthless gang of Bad Blood Predators who controller Xenomorphs. The fight against the Queen didn't start well, with several Yautja and Colonial Marines dying. However, the Queen was captured, kept in chains, and brought near the Killer Predator controller Xenomorphs, to gain them back to her side. This mission was successful in the end, and the Queen became the leader of the special breed of tusked Xenomorphs.
Hunter and Warrior Predator vs. Alien Queen Mother
During the infestation of San Drad in the Alien vs. Predator Arcade Game, the Hunter and Warrior Predators came to Earth to clean out the Alien menace. After taking down hordes of Xenomorphs in the city, they encountered the Alien Queen Mother and her eggs in a building turned in to Alien hive. The Queen was still attached to her egg sack and wasn't difficult to deal with. However seemingly dead, she survived and followed the Yautja hunters. The second fight occurred on the ship of General Bush, a madman Colonial Marine with ties to Weyland-Yutani. The Queen ripped Bush in half and engaged the two Predators again. This was the end boss fight of the game and more difficult than the first one. The Predators prevailed, crashed the ship into San Drad, and saved Earth from the Aliens.
Prince vs. LV-1201 Queen
When Prince Predator descended the Engineer ruins at the end of Aliens vs. Predator 2, he met the Alien Queen at the place where the ruins molded into an Alien hive. The place could have been better suited for a Praetorian guard. The fight was somewhat anti-climatic, as Prince was really after Vassili Rykov, who was at the bottom of the hive wearing a Colonial Marine Exosuit. The Queen was killed using the various weapons and Prince's disposal, but there was no trophy taken as the Yautja only cared about Rykov and his stolen bio-mask. The game also included an Alien Empress, but neither the Colonial Marine nor Predator character could fight her.
Top Knot's Clan Capturing a Queen
Topknot's clan capturing a live Xenomorph Queen from a hive on an unnamed world at the start of Aliens vs. Predator: War is a spectacular sight and the first case of a Queen being captured by the Yautja in the AvP lore. The fight preceding the capture involved the Queen sacrificing waves of Xenomorph drones for defense and some of the Predators dying as well. When the Queen was brought to the Predator ship, she made a final attempt at escape but the clan was saved by Machiko Noguchi, a human hunting together with the Predators. Machiko took the place of a fallen Predator and distracted her long enough for the makeshift prison door to close on her. The Queen was captured and was ready to produce Xenomorphs eggs for the Predators.
Unnamed Predator vs Caverns Queen
The ending boss fight of the Predator campaign at the end of the Aliens vs. Predator 1999 PC game is an honorable one by Yautja standards - all energy weapons of the unnamed Predator were switched off and he could only use his melee and speargun. The Queen had the help of some facehuggers and the confined space of the caverns on the undisclosed planet. The Praetorian warriors guarding her were already dispatched in the previous level. The Predator was able to shoot off the tail of the Queen before finally mortally wounding her. In the end, the Yautja stood over his new trophy and roared his victory cry.
Dachande vs. Ryhushi Queen
The Dachane vs. Ryushi Queen fight from the Alien vs. Predator comic series is one of the first and well-known brawls for the two creatures. After the Xenomorphs had infested the Ryushi colony, the Queen set up a hive in the Lector, a commercial transport vessel. Dachande teamed up with Machiko Noguchi to take her down. After trading blows, Dachande was mortally wounded, but the Queen got her head stuck in a door and it was severed. Before dying, Dachande blooded Machiko with a severed finger of the Queen and her head was taken by Machiko as a trophy and set on top of her new house.
Smiley vs. Temple Queen
A lone Predator going against an Alien Queen has happened several times in the AvP games, but this is one of the rare cases of it happening in the comics. Smiley's clan was previously wiped out by the Alien swarm, so he wanted revenge. After dispatching several Xenomorph warriors, he reached the Queen in the catacombs of the ancient temple. We don't see much of the ensuring fight, but Smiley emerged bloody, with one remaining eye, and victorious. He had also taken the Queen's tail as a trophy. Smiley was a great Predator and was also included in the list of the most underrated Predators.
Scar Predator vs. Antarctica Queen
The Scar vs. Antarctica Queen fight from the ending of Alien vs. Predator 2004 is the first and last time we have seen these creatures fight on the big screen. After escaping from the Yautja self-destruct in the underground temple, the Queen emerged unharmed. Scar was missing his shoulder cannon and used his other projectile weapons on her, but only managed to wound her. Scar and Alexa Woods managed to chain the Queen to a water tower, that was dangling over a cliff. Before she fell over, she stabbed Scar through the chest, somehow missing the Predalien chestburster inside. Scar died a few moments later and the Queen plunged into the cold depths of the Antarctic waters.