After some discussion in general, I think I've narrowed down what the actual problems are with the Mr. Peterson fight in the museum. To put it simply: the fight fails at satisfying some core game design principles of what makes a good boss fight. The segment plays out like a regular segment of the game, with no changes other than a speedy Mr. Peterson. Good boss fights are intended to challenge you on the mechanics and skills you've learnt throughout the game up to that point, giving the players a brand-new challenge that they have to use their skills to overcome. The Ted fight is pretty much the exact same thing the player has been doing over the course of the game with little to no changes.
To put it simply, the Ted fight needs to take a standard segment of gameplay and add something new to it. It needs to flip it on its head in some way to challenge the players on their stealth, parkour, and puzzle solving skills, while being just difficult enough to satisfy the needs of being an "Act 1" boss instead of a FINAL boss. I don't know specifically what that would be, but generally, this is the problem with the boss fight.