Seems like I have to do some tweaking… But what? 
You should probably slow down or add some delay between layers as the amount being printed per layer decreases. I’m not sure about other slicers but slic3r has a setting for that.
And on closer inspection, you may be over extruding.
If you’re just getting up and running I wouldn’t recommend this test
Print some 5mm calibration cubes and get your jerk accel and speeds right. Then adjust extrusion.
The extrusion isn’t great but for tests you should be fine. Notice how your top flat layer isn’t totally filled
It’s possible simply that radiant heat from the hot end nozzle is keeping these from cooling appropriately. Rather than slowing down (and injecting MORE heat into this), try a fan. Try insulating the block with something like E3D’s nozzle sock (if you’re using an E3D).
Basically, without more information on your setup, we are all just guessing.
Can you tell us what kind of printer you are using, what diameter nozzle, do you have a heated bed, are you using a fan to cool your print, what kind of plastic, at what temperature are you printing and any information about how you sliced the model.
Could also be slicer related: I remember doing that same print back in the day via Makerware (on my Rep1): When the tips got infinitely small at the top, it had a hard time handling that geometry and ended up over-extruding in a similar (but different) fashion. When I did the same thing in Simplify3D, it handled it correctly and I got a better result.
Home made printer, direct extruder, original e3d v6, 0.3mm nozzle, ABS@ 230°, bed@ 100°. 0.15mm layer height, Simplify3D: 1.7 mm retraction, coast at end 0.3mm, whipe nozzle on outer perimeter
Not enough cooling / time between layers which is why it gets worse nearer the top. Print a tower next to it so the spikes have enough time to cool between each layer.
Or print several of them at once – four of them would give each layer time to cool for example.
