The largest nuclear weapon ever detonated was the Tsar Bomba.
It was a fission-fusion-fission device which used layers to magnify the bombs power.
One implication of such a device is that you could scale such a device up further. There's some kind of a limit where above a certain size light from the first stage blows the later stages apart before they can actually ignite but nobody is quite sure exactly where that limit is.
It might be possible to build a bomb weighing many tens of thousands of tons with a yield in the range of of hundreds of gigatons.
Detonating such a device high in the air would be a bit pointless since the horizon sets a sort of limit: you end up just ejecting a chunk of the earths atmosphere within line of sight into space and a bigger bomb just means ejecting it faster.
but, for comparison the impact that wiped out the dinosaurs was on the order of 23,900 gigatons.
So a few hundred gigatons is definitely not enough to destroy all life on earth. And life is surprisingly durable, you'd need the kind of energy needed to liquefy much of the crust. Just for arguments sake lets guesstimate that you'd need something 100 times larger than the asteroid that killed the dinosaurs to kill every bug and critter on earth.
So lets round it off to 2,390,000 Gigatons needed.
lets assume you solve the problem of building an arbitrarily large nuclear weapon, you solve the problem of the early stages tearing apart the later stages and come up with a design that you can scale up smoothly.
The Tsar bomba design appears to have a limit of about 4 megatons per ton yield, you need to add 1 ton to the bomb design per 4 megatons of bomb yield.
So your world-killing bomb will need to weigh something like 597,500,000 tons.
At this point your evil mastermind would need to be buying large fractions of the entire worlds metal production and years worth of the entire worlds nuclear material production to get enough raw materials. It would be very very hard to be stealthy about it.