I think the terrorist threat of nuclear weapons may be under-estimated. There are some
claims that even reactor grade uranium and plutonium could be made into nuclear bombs. They would not be efficient, but they could yield up to a kiloton, more than enough to take down
one or more skyscrapers.
As for large bombs, there is really little reason to do it. I'm not sure that it is impossible to make a one gigaton bomb... maybe a modified layercake multistage device could eventually deliver a yield that large through a series of steps, but I doubt it. It's more destructive to use several smaller bombs than one large bomb.
Even then, I don't think we'd actually be able to destroy all multicellular life on the planet directly. With a 5psi overpressure blast radius for a 200-kt airburst we'd need almost 1 million devices to blast every square mile of US territory. With a 500-KT airburst we'd need over half a million devices. With a 1-MT airburst we'd need over 338-thousand devices. Of course, animals burrows that are more than a few feet underground will survive at dramatically closer radii.
The above used a 5psi overpressure, but the
published overpressure lethality threshold (not from impact from or against objects) for humans is actually 10psi. The radii for 10psi are: 2.8mi for 1MT, 2.2mi for 500KT, and 1.6mi for 200KT.
Radioactive fallout is harder to figure because you need to take into account the type of device, the yield, the location of the explosion, the winds and weather, the biology of the individual species, the time since the explosion, the area of deposition, the amount of time spent in the radioactive zone, the decay rate of the fallout and any mass shielding the animal might have from its habitat. Due to the shielding ability of water, it's unlikely we could ever kill off ocean life.