The Doctor

What regeneration he's up to is deliberately vague, but the Doctor is at least a thousand years old by the time we meet his current form. He sees being 'last of the Time Lords' as a responsibility more than anything else, and as such, he's more likely to go looking for bad guys who need stopping rather than just exploring the universe and waiting for bad guys to turn up. His outfit—grey suit, black cloak and brown fedora—was described by Matthew as a mashup of Sherlock and Indiana.

• Badass Boast:
  "I'm the Doctor. Last of the Time Lords. Sole custodian of History and Creation."
• Sherlock Scan: He pulls out this trick more often than previous regenerations did.
• Time Police: The Doctor has shades of this, having come to believe he's responsible for the universe and recognising the dangers of inexperienced (or worse, malicious) time travellers running amok.

Matthew Hall

A Detective Inspector from London who winds up investigating an alien takeover. The Doctor met a future incarnation of Matthew—a Badass Doctor-like time-travelling hero who fights monsters and helps the helpless as a result of his adventures with in the TARDIS—before he met the contemporary Matthew, who he subsequently invited to travel on the TARDIS.

• Action Survivor / Badass: He goes from the former to the latter over the course of the story.
• The Hero's Journey
• The Watson: To the Doctor.
  • Heavily lampshaded when the Doctor and Matthew meet Sir Arthur Conon Doyle.

"Loki"

A "cousin" of sorts to Fenric, the being of chaos known as Loki is one of the Old Ones who was bound in a transdimensional prison after this universe came into existence. After billions of years in captivity, her 'shadow' has managed to escape: it flits across the Universe and sews whatever chaos it can, "nudging" the rules of reality to create unpredictable, destructive situations (albeit with only a fraction of the power she'd have if she was really free).

• Chaotic Evil: Technically. She's not actively malicious, but of Loki ever escaped and went on a chaotic rampage, she'd eventually break down the laws of physics and unravel the space-time continuum.
• Distracted by the Sexy: While Loki is technically genderless and can appear as anything or anyone, she mostly shows up as a beautiful woman in an attempt to invoke this trope. Because let's face it, there's a history of beautiful women sewing chaos.
• The Trickster: Well, duh.

Commander Tenodis

Commander of an alien warforce, he went insane after forty years in UNIT's captivity before breaking out and trying to steal the TARDIS to escape Earth. He escapes with the help of Loki (albeit without realising at the time), and is later recruited to help destroy the Doctor, Matthew and contemporary Earth.

• Animal Assassin / Bond Creature / Beast of Battle: Tenodis' people don't command soldiers so much as they have telepathic control over creatures bred for war. 'Flyers' are pterodactyl-like creatures that breathe stream of fire so hot they burn metal; 'Tanks' are slow, but their hides are near impenetrable and they can 'burp' highly-explosive matter over half-a-kilometre in distance.
• Ax Crazy
• The Lone Dalek: Averted.
• The Mad Hatter