The invisible monster smacks the Doctor with its giant tail, and then the Doctor helps Vincent fight the monster, which means generally that the Doctor gets knocked around several times while cutely swinging a stick at nothing in particular. Vincent chases the monster away, and the Doctor continues fighting windmills for a bit, and then back inside Vincent paints over a very famous canvas of some kind -- Amy nearly hurls with horror -- so he can sketch out exactly what an invisible rooster monster looks like. It's quite detailed. The Doctor's like, "Well, hell."
The Doctor heads over to the TARDIS to find some kind of technology, after distracting Amy and Vincent with a variety of cute facial expressions and his particular brand of sexy silliness turned up to about a hundred. The thing invisibly chases him inside and he finally finds the device, which is like an iPad made of bicycle parts that identifies things you put in front of it. Like he sticks out his tongue at it, and it starts throwing up pics of him from One to Two and Three. He shows the device -- "an embarrassing present from a dull Godmother with two heads and bad breath" -- Vincent's sketch, but it doesn't work. "This is the problem with the Impressionists! Not accurate enough."
Outside the TARDIS, heading back through town, the creature looms behind the Doctor, showing up on the mirror-screen, and it identifies the monster for him. Of course he doesn't know it's behind him, because huge invisible roosters are super stealthy, especially when -- spoiler -- they are blind. "You poor thing," he says, "You brutal, murderous, abandoned thing. I hope we meet again soon, so I can take you home." Short chase, of course, immediately follows.
Amy scares the Doctor around a corner, explaining that van Gogh's snoring is driving her crazy. They buy him a courtyard full of sunflowers, to inspire him or something, and feed him breakfast. Vincent on sunflowers, and this is awesome: "It's not that I don't like them. I find them complex. Always somewhere between living and dying. Half-human, as they turn to the sun. A little disgusting. But, you know, they are a challenge." You could build a whole episode around that little speech. Maybe at some point they did. Inside, the Doctor shows him the creature -- "...The eyes, without mercy" Vincent nods -- which is called a Krafayis.
Their deal is that they travel in packs, through space, scavenging. When one gets left behind, they don't come back, because they are a brutal race. There is a stigma. So all around the universe there are these merciless, utterly abandoned Krafayis singletons, who kill and kill until they are killed, which doesn't happen because they are invisible. Which is all quite interesting because that's so one-sided -- like the one-dimensional Silurian assholes -- that you wonder how on earth they're going to make any kind of point at all when they finally meet with it. Well, I'll tell you: They won't. There are so many awesome things about this episode, but one of them is not this. So just forget everything I just told you about the Krafayis, because none of it matters any more than the rules from "Blink" could have helped at the Byzantium.