Earth's diameter: 2,123,000 levels (6 meters high each)
All of the rest of these numbers were arrived at using the Generic Nuclear Weapons Formulas on page 177 of Interstellar Operations. No real physics were harmed (or even consulted) during these calculations. I hope you all enjoy :D ;D
Nuclear Weapon needed to crater that many levels, punching a hole all the way through the planet:
30,000,000,000,000,000,000,000,000 kilotons (3E+25)
This would do:
6,000,000,000,000,000,000,000,000,000 Standard scale damage (6E+27)
In a radius of:
7,768,081,264 hexes, or 456,945,957 map sheets
If exploded in the air instead of on the ground it wouldn't crater through the earth (rules say so), but it would explode in a radius of:
10,331,548,081 hexes, or 607,738,122 map sheets
It would lose damage at a rate of:
772,391,507,772,466,000 per hex if exploded on the ground, or
580,745,494,565,764,000 per hex if exploded in the air.
Secondary effects would have a radius of:
15,536,162,528 hexes or 913,891,913 map sheets, if exploded on the ground, and
20,663,096,162 hexes or 1,215,476,245 map sheets, if exploded in the air.
The Height of the Secondary effects would be:
If exploded on the ground, 863,120 Space Hexes past the ground row on the Space Map, or if exploded in the air, 1,147,950 Space Hexes past the ground row on the Space Map. That is far more than enough to irradiate the moon as well.
The Height of the primary damage would be:
From a ground explosion, the damage would reach 431,560 Space Hexes past the ground row on the space map, and for an air explosion, it would reach 573,975 Space Hexes past the ground row on the space map. Now while the rules don't let allow for cratering another celestial body, that means if you can line up the damage, you could turn then entire moon to a crisp with this explosion as well... and even things well past it.
The Critical Hit Chance of this explosion is:
Amusingly it will only score a critical hit on a 4+, so other than being utterly erased from existence, at least you might not get crits from it.
This warhead would weigh a measly:
15,000,000,000,000,000,000,000 tons (1.5E+22)
Unfortunately none of this is legal, because the maximum legal Nuclear warhead yield is 50,000 kilotons... far less than what is needed to actually destroy the Earth in battletech.
I hope you have all enjoyed today's educational piece from the Department of Mega-Engineering.