P.S.

So, let's parse complex case: "Я никогда ничего не буду недооценивать".
Well, we have 4 no-particles here. "не буду" (will not) tells us we have negation, so we convert ни-words to opposites: никогда(never)->always, ничего(nothing)->anything. недооценивать is "underestimate", "не-" is direct negation of "estimate" and nothing need to do with it.
So we get: "I will not underestimate anything at any times (always)". Which is shortly "I will never underestimate anything" in english I believe.