This is far too strong for a common. Easy first pick, for almost no cost it destroys tons of stuff. Honestly, I'd still first pick this in Scars draft.

I lowered toughness and increased costs. Still too powerful?

This seems comparable, but still better, to Royal Assassin. As a general rule of thumb, I'd say repeatable creature destruction should be uncommon, and repeatable creature destruction without depending on a limited resource (sacrifice a creature, discard a card, etc) should be rare.

Would a Teselecta Antibody be equally well represented by a card that had to sacrifice itself to destroy something? That can be strong, but can still be common?

Yes, still way too powerful for common and probably for uncommon. This is pretty close to Avatar of Woe's ability, which was a deck-defining casual card.

Here are the common Assassins in printed Magic. Three of them are one-off killers with a restriction. The other one is a repeated effect, but it's a temporary -1/-1. Most of the uncommon Assassins are oneoffs as well, or very restricted like Hunter of Eyeblights.

Given which, Jack's guidelines seem very accurate to me.

Ah, spellshaping Terror. That's Notorious Assassin. Still rare, I'm afraid.

if this is an enemy of the doctor why not just make it able to target the doctor's colors? Or whatever colors are enemies of this creature in teh show. My point is it's still probably too strong for an uncommon honestly. Turning useless lands into terrors is great. If you don't like selective targeting of colors, try maybe making them discard 2 cards. That would be enough to play this at uncommon I think, with it sucking up that much fuel.