Note: The numbers here are very rough, and really only good to about an order of magnitude. They just give us some idea of what the Red Death is capable of.
In the first How To Train Your Dragon film, the Red Death, a massive and powerful dragon, rams through a mountainside before attacking the Viking army. The Vikings fire catapults at the beast, but the rocks are basically completely ineffective, and Stoick throws a big wooden stake at its head to little effect. Let's figure out how powerful those catapults and stakes are, giving us a lower limit for the Red Death's durability. Because I'm looking for a lower limit, the numbers here a generally minimum.
The size of the rocks
The rocks appear slightly larger than the Red Death's eyeballs, which are about six feet in diameter. I'll assign them a diameter of 2.5m.
The velocity of the rocks
The creators of the movie wickedly conspired to only show the catapults firing in shots with no side-on view, so I can't get their speed with even the low level of accuracy I'd like. However, I can say with confidence that they are going faster than 10 m/s.
The mass of the rocks
If the rocks are made of granite, which has a density of 2691 kg/m^3, then they weigh approximately 8m^3 x 2691 = ~20000 kg. This is about as much as two very large elephants.
The energy, momentum, force, and pressure applied
1/2 x 20000 x 10 x 10 = 1000000 J (1 MJ).
20000 x 10 = 200000 kg*m/s
1/2 x 20000 x 10 x 10 ÷ the distance to stop (which I guesstimate at 3-12 inches) = 3000000-10000000 N
If the area of impact is 1 square meter, then the pressure is 3-10 MPa.
Now for the stake.
The size of the stake
It's pretty close to about 2 meters long and maybe 4 inches (0.1 m) thick. I'll call it a cylinder for the sake of simplicity. This makes it, assuming a density similar to Douglas fir wood at 530 kg/m^3, about 11 kg in mass. Dang, that's a heavy stake.
The velocity of the stake
I can get this to more accuracy than with the rocks. It takes 1 second to get up to the 100-ft-tall Red Death's eye. Using the Pythagorean Theorem, I find that the distance is about 112 ft, and therefore the velocity is 34 m/s. (This may be an underestimate.)
The energy, momentum, force, and pressure applied
1/2 x 11 x 34 x 34 = 6400 J (6.4 kJ)
11 kg x 34 m/s = 374 kg*m/s
1/2 x 11 x 34 x 34 ÷ 0.0762 or 0.3048 = 21000-84000 N
Assuming an impact area of 1 square cm, the pressure at the impact point is 210-840 MPa.
Conclusion
The Red Death is very durable against both blunt and piecing attacks. MJ-level attacks do not seem to bother it at all, and its skin can withstand 210-840 MPa with ease.
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