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Galen's second incarnation was born from an act of heroic self-sacrifice which saved billions of lives. When a faction of the Time Lord High Council tried to destroy an inhabited star system, in order to alter the course of history and aid the Rutans in their battle against the Sontarans, Galen gave his first life to stop them. The scheme came terrifyingly close to succeeding; it was only the help of his second incarnation, crossing his time line to create his own future, which allowed the first Galen to defeat it.
He gained powerful enemies in the process. The Time Lord Councillors responsible for the scheme had been acting illegally; such blatant interference in the time line, with such genocidal consequences, would have led to their exile at best and execution at worst. They dared not take the chance that Galen might be recaptured by the Time Lords and reveal the truth. They knew that they would never be safe until he was dead. Their efforts to hunt him down were hampered by the untraceable nature of Galen's TARDIS and their inability to use official resources to pursue him, but they made up for that with a determination born of desperation.
Although older and wiser than his first incarnation, Galen's objectives haven't really changed - they could essentially be summed up as "have fun and help people", although "and stay off the Time Lords' radar" is an important addendum.
Cheerful, friendly, and sometimes a little bit boisterous, this Galen is protective big brother for those who need help, and a boon companion for those who just want to sit down and have a few beers. His formidable intelligence and tremendous technical skills are rarely apparent at first glance. Many of his opponents have underestimated and disregarded him after seeing him happily wading into the thick of a bar brawl, or performing (very bad) beer-fuelled Karaoke - usually much to their later regret.