Number 1 should say... It is embarrassing the extremes THAT he will go to in order to IMPRESS his boss. Number 2 should say... It is embarrassing THAT he will go to extremes in order to IMPRESS his boss.

"Express his boss" makes no sense unless you mean to say he will grind up his boss and turn him into coffee. Both sentences could achieve improved clarity by introducing punctuation and some tiny extra words. In both sentences, "it is embarrassing" needs to be set off somehow from what follows. Without punctuation, saying "it is embarrassing the extremes" makes it sound like "the extremes" are being embarrassed. #1: Place the preposition "to" next to its object: "It is embarrassing, the extremes to which he will go in order ..." #2: Since you are highlighting the magnitude of the extremes, you should to say "such extremes" rather than "the extremes". Also, to set off "it is embarrassing" from the rest of the sentence, you either need to create two separate sentences or use "that" as John B has suggested. Also, "would" is better than "will": "It is embarrassing that he would go to such extremes in order ..."

We normally say: the LENGTHS he will go to. Otherwise what others have said about the grammar I agree with.