Neutron Bombs On the neutron bomb: The biggest advantage to this is it avoids
collateral damage, harming only biological components. This means that its effect would likely pierce through Lavos' shell (most shells have few organic components in them) and hit the core directly.
That's not quite how a neutron bomb, or enhanced radiation warhead (ERW), works. An ERW is a small atomic bomb which has been modified so that neutrons created during detonation are not contained within the device, but allowed to escape, producing an intense burst of radiation. ERWs were intended to be used against armoured forces because tanks are resistant to the blast and heat of a nuclear weapon, but only offer limited protection against neutron radiation. An ERW is not any less destructive than a conventional warhead.
Living things and electronics are more vulnerable to radiation than other materials due to their intricate components, but non-organic materials are not transparent to neutron radiation as you seem to suggest.
AntimatterSome Calculations
1 Ton of TNT = 4.2 * 10^9 J
100 trillion Ton of TNT (1e14) = 4.2 * 10^23 J
The annihilation of 1 kg of matter with 1 kg of antimatter yields
E = mc^2 = (2 kg)(3 * 10^8 m/s)^2 = 1.8 * 10^17 J
An explosive device equivalent to 100 trillion Ton of TNT would require about 2.3 million Kg of antimatter.
Antimatter production is currently very costly and inefficient. Antimatter is also difficult to contain. The production of 2.3 million Kg of antimatter, let alone containing this amount with sufficient density to produce an effective weapon would be a scientific and engineering marvel far beyond our capability.
To put this into perspective, CERN can produce about 10^7 antiprotons per second.
There are 6.02 * 10^23 antiprotons in one gram of anti-hydrogen.
To produce one gram of anti-hydrogen would require
(6.02 * 10^23) / (10^7) = 6.02 * 10^15 seconds (1.9 Billion years!)
Guardian_of_Ages, 90 MJ is about the energy released by the combustion of 2 Kg of gasoline, which isn't very much at all.
Physical Properties of Diamond and Lavos' ShellDiamond is the hardest known naturally occurring substance and has good physical properties, but it is not some sort of magic material. Diamond will actually combust at about 800 degrees C. Any quantity of diamond incorporated into a nuclear warhead will be instantly vapourized by the explosion.
The K-T impact vapourized, melted, or ejected over 200 thousand cubic kilometers of the earth's crust, producing a crater 180 kilometer wide and several kilometers deep. The object penetrated 15 kilometers into the earth before being almost completely vapourized. If Lavos survived this type of impact, it's shell must be far more durable than diamond. Leebot mentioned Neutronium, which would have sufficient physical properties. Lavos' shell could also be a magic material, like the elemental weapons and armour produced in Zeal.
I don't think that Lavos' shell was destroyed by the impact, because it appears to be an integral part of its body. It may also need its shell to protect it form the extreme temperature and pressure in the core of the earth.
StrategiesGamaray lasers, as mentioned by Hadriel, are promising. A nuclear warhead can be configure to produce an intense, focused burst of Gama radiation (a Gama-ray laser) which may have some effect on Lavos.
It may be possible to produce miniature black holes in a particle accelerator. I'd like to see Lavos deal with a stream of exploding mini black holes.