려고 들다

be bent on doing something

"-(으)려고" (intending to) plus 들다, which adds eagerness and pushiness — not just meaning to, but going at it. It usually carries disapproval: he's always trying to lecture people, why are you out to hurt me, they'll try to inflate GDP artificially, they'll move to withdraw it. Two lines here only look like this construction and are not: 뭐 하려고 들고 있나 is 들다 "hold", and 느끼려고 드시는 건 is 드시다, the honorific of "eat".

Register: often disapproving