Third part of the series. I have one more part planned for this, although if it is a bit long I might split that part into two more. I know exactly where this is going and I'm actually pretty excited to get it in writing, so once I post this, I will write out the fourth part, making sure the twist is as good as can be. If you haven't read parts one and two, they are in my sig. Hope you all enjoy.

As the giant footsteps draw closer, I dart to my right,
and stumbling over broken headstones, I grab hold of a sturdy branch
and hoist myself into the tree and wait. The footsteps stop beneath me.
The darkness clings to my skin, capturing my breath in cold claws,
sucking it from my lungs. For the middle of summer, it's fucking cold.
The man below me moves off deeper into the cemetery
and as he does so, I gaze up through the middle-aged leaves
and sample a glimpse of a starry sky, the first time I've seen it here.
What I've seen so far tonight briefly escapes my memory
as I stargaze, searching for constellations I learned at school.
A cloud moves in and spoils my view.

I listen in the black of the night for the man chasing me so vehemently,
but there is nothing. Even the birds have been scared off.
I climb down from the tree, careful where I place my feet
and begin to head for the flat again when I spot him at the exit, waiting for me.
He's surveying the resting place of the dead, hoping to glimpse me.
I duck behind a headstone and peek my head around the side of it.
We make eye contact. He runs towards me screaming.

I leg it in the opposite direction, hoping beyond all hope
not to lose my footing or desecrate a lump of granite or marble
marking the body of a man who died a lot less morbidly than I'm about to.
The cold air spikes at my throat and it makes me cough.
I might as well have an arrow above me pointing at my skull
with "Lunch Is Served" above surrounded by flashing lights.
I dive into a bush and come out the other side swearing excessively
as I pull the thorns from my arms whilst trying to concentrate on straight ahead.
Another tree. I joist myself branchward, and as I cling for dear life
small branches fall to the ground after being kicked by my flailing feet.
I climb another branch. Below me, he screams for me.
"Help!" he seems to say. I look around befo...wait, what?

I look down on him and he seems to look different from before,
the bloodthirstiness replaced by need and frustration.
Although that may be the darkness playing tricks on my eyes.
He seems to plead with me to come down but I hold firm
which seems to upset him a little. In vain, he grabs a headstone
and begins to pull at it. In a matter of seconds, he snaps it on two
and hurls it towards me. It smashes through the branch I'm sitting on
just a couple of feet to the left of me, and I fall from the tree
and land on my side. As I lie there dazed and confused,
he hurries over and picks me up by the armpits so we're at eye-level.
He stares deep into my eyes and, once again, utter the word help.

You definitely brought that atmosphere back that was missing. I'm wondering where this twist is going though, I'm hooked. Hurry up and bring MOAR!
There's not much that I can add here. The execution was filled with confidence and had an interesting plot. I also did like how you kept this in character, in the entirety of the piece; which made this more like a poetic prose which I'm sure was your aim all along. The last stanza though, did feel quite anticlimactic for what it was, but I guess it also did act as a steady cliff-hanger for the next instalment.

Nicely done!

PS: If you have time please check out my latest piece called “Concordant”. Here's the link: https://www.ultimate-guitar.com/forum/showthread.php?t=1151671 .
A quick comment would definitely suffice.
Thanks guys. The next part is the last, as I've just finished it. I'll be conferring with my flatmate, who incidentally has written a short story based on this with slight differences, the main one being that his is told from the viewpoint of "Ajax". The ending to this is slightly anticlimactic only because of the next part. I felt the sudden change of persona of Ajax was sufficient enough to be an endpoint to this.