Against the Doctor
The Eighth Doctor and Izzy encountered Destrii inside a gargantuan, snake-like spacecraft known as Ophidius that had swallowed the Doctor's TARDIS. Destrii survived on her own inside the belly of Ophidius for quite a while. She was being pursued by the aliens that controlled the world-snake.
To evade pursuit, she tricked Izzy into using a machine which placed their minds in each others' bodies. Destrii tried to pose as Izzy and escape with the Doctor in the TARDIS, but the Doctor, observing her violent tendencies, saw through the deception. Before he could do anything to reverse the mind switch, Destrii, in Izzy's body, was apparently disintegrated by a member of the predatory, intelligent species, the Mobox. (COMIC: Ophidius)
While Izzy was adjusting to the trauma of being trapped in an alien body, she was kidnapped by representatives of Destrii's mother, the Matriax Scalamanthia of the planet Oblivion. Retracing his steps with the help of former companion Fey, the Doctor found Ophidius anchored in the skies above the Mobox homeworld and Destrii alive in its jungles. The Mobox could retain the patterns of those they disintegrated and reconstitute them. B'rostt, the Mobox who had attacked Destrii, had reconstituted Destrii and left her in the jungles to die, later to build a new empire on his planet. Destrii, however, was made of sterner stuff and had survived, even in Izzy's body. The Doctor took Destrii with him, determined to find Izzy and restore his companion to her rightful body.
On Oblivion, the Doctor discovered that Destrii belonged to a race that had been genetically manipulated so no two individuals were alike. Generations before, the people of Oblivion had looked human. The ruling families had attacked their enemies with a plague that stripped its victims' minds bare. The natives had sealed themselves up to wait out the plague's progress. They found the victims had been transformed into living generators of psychic energy who shared a gestalt consciousness. The Horde, as they were now known, transformed the ruling families into animalistic humanoids for their sport and sealed Oblivion from the rest of the universe.
Discovering that Destrii was in Izzy's body, the Horde representatives who had kidnapped Izzy switched them back. Destrii and Izzy saw into each others' minds during the transfer. Izzy saw Destrii was the daughter of the ruling Matriax, whom the Horde still deferred to. However, Destrii had also been raised in the arena, fighting death duels all her life. She was feared by everyone except her uncle Jodafra, who looked like a humanoid lion. Jodafra had built a chronon capsule that Destrii had used to escape before, but the Matriax brought her back to be wed. When Destrii refused, the Matriax beat her. Pushed beyond tolerance, Destrii killed her mother. The Horde descended on Destrii, choosing her as their new leader and transforming her into a psychic energy generator as well.
Destrii prepared to destroy the cities of Oblivion with her newfound power but Izzy reminded her she wished to be free and urged her not to become one of the monolithic Horde. It turned out Jodafra had allowed Destrii to escape to prove his chronon capsule sound. While the Matriax and the Horde searched for Destrii, he had perfected a device to drain the Horde to power the capsule for his escape. Realising she has been used, Destrii poured her own energy and the Horde's into the capsule, reverting to her amphibian form and giving her uncle and her the ability to roam time and space. (COMIC: Oblivion)
The Doctor next met Jodafra and Destrii in North America in 1875 near the Lakota village led by Chief Sitting Bull. Jodafra had made an agreement with the Windigo to feed it human flesh in exchange for help navigating the time stream. Destrii realised Jodafra meant to sacrifice Lakota children to the Windigo,. She destroyed the equipment that supported the spirit, allowing the Doctor and the Lakota to defeat it. Enraged, Jodafra beat Destrii nearly to death, leaving her unconscious body in the snow and departing in his capsule. The Doctor found Destrii and took her to Hippocrates Base, a space station hospital, to heal. (COMIC: Bad Blood)
With the Doctor
Destrii helped the Doctor repel a Zeronite attack on the base. While the Doctor acknowledged that Destrii was an "egocentric, immature hellion" with a violent streak "wider than the Gobi Desert", he also felt there was a decent person underneath. He offered her a second chance and to show her the universe if she would stick to the rules. Destrii accepted gladly. (COMIC: Sins of the Fathers)
One of their first trips together was to Earth, where Destrii wore a holographic disguise that made her look human, she accidentally offended a Chinese stallholder. She killed many Cybermen when taken aboard the Cyber-ship with the Doctor. After defeating the Cybermen, the Doctor landed the TARDIS in a field and together they walked off into the distance. (COMIC: The Flood)
Destrii took a "fists first, brains second" approach. She was horrified by Jodafra'a actions in America, spurring her to act against him. (COMIC: Bad Blood) She was, on occasion, racist, but did not mean offence. She was extremely agile, showing remarkable combat abilities and knew much of popular Earth culture, but was initially unprincipled and quick to violence. (COMIC: Sins of the Fathers, The Flood)
Behind the scenes
According to Panini Books' graphic novel reprinting of The Flood, Doctor Who Magazine intended for Destrii to witness the Doctor's regeneration into the Ninth Doctor (in an unpublished alternate ending to The Flood) and travel with the Ninth Doctor in a series of stories set before Rose. The BBC, while they approved the comic strip depicting the regeneration, vetoed any "Year One" stories with the Ninth Doctor and Destrii, on the grounds that the Ninth Doctor could not be shown in the strip before he had appeared on television, and the new Doctor had to be accompanied by Rose Tyler in all of his comic strip appearances.
As a result, Destrii's ultimate fate has yet to be chronicled in any official media. It wasn't until 2008 that DWM's comic strip featured an original companion again with Majenta Pryce. The Ninth Doctor, meanwhile, would finally get a non-TV companion, Ali, in the 2013 Puffin eshort The Beast of Babylon. In retrospect, the events of The Night of the Doctor would have made Destrii's continuation between the Eighth and Ninth Doctors (not to mention the planned regeneration depiction) difficult to reconcile with TV continuity had it occurred.