extremely bad at; dread; really dislike
Emphatic phrase for something one is very poor at or strongly averse to. Often used with ～が大の苦手 or ～は大の苦手.
I'm really bad at speaking in front of people.
He really dislikes getting up early.
Combination of 大の (great, big) and 苦手 (weak point, dislike). The exact historical derivation is uncertain, but it functions as an emphatic set phrase.