If the attacker scores two or more hits...
if the attacker scores more hits than the BR of the target (or two for Elizabeth)...
This means that two hits will always kill a general with a BR of 0 or 1.
Three, or more hits are required to kill a general with a BR of 2 or Elizabeth.
In all of these cases, it's not sufficiently clear that you mean to reference the amount by which the number of attacker hits exceeds defender hits.
This is sort of a similar procedure to debates in HIS (ex: if you get two net hits against a level 2 debater, you don't burn/disgrace them).
This part is right on the money.