Belanger dances with an (i)__________ that draws one’s attention as if by seeking to (ii)__________ it; through finesse and understatement, he manages to seem at once intensely present and curiously detached.

It is difficult to fill the first two blanks without reading the sentence fully. In fact the clues for both the blanks are present in the second part of the sentence after the semicolon -

"through finesse and understatement, he manages to seem at once intensely present and curiously detached".

The above states the method of dancing - finesse and understatement - and how he goes about seeking attention - by being intensely present and curiously detached (at the same time).

We now have all the clues to crack the puzzle.

Since he dances with finesse and understatement, the word for the blank should be undemonstrative panache. One could argue for unattractive gawkiness since his style was one of understatement, but then we know that he danced with finesse - impressive delicacy and skill. And finesse is the exact opposite of gawkiness - nervously awkward and ungainly. And unrestrained enthusiasm is the exact opposite of "finesse and understatement".

The second blank talks about how he draws one's attention. Now, we know that he manages to seem "intensely present" and "curiously detached" simultaneously.

Therefore, it cannot be "by seeking to focus" or by "seeking to overwhelm". But it is definitely "by seeking to deflect".