デジタル大辞泉 has a relevant definition in its entry for the verb "攻める".
So "攻めた格好" would mean a fashion style that is 積極的 -- 'bold', 'daring', 'enterprising' -- rather than 無難 -- 'tame', 'conservative', 'playing it safe' -- though it does not necessarily implicate the sense of extremeness or impropriety as I think "outrageous" does.
And I'm pretty sure that is the sense in which "攻めた格好" is used by the character and in which "攻めた服" is used by the people who assigned that label to the images you found.
The problem is that even if the sense or definition of a word/phrase is agreed upon, the matter of what things actually fit that definition may be left to subjective judgement. In such cases, trying to figure out the meaning of the word/phrase from things it is applied to can be a less-than-ideal way.
Even though people share the same understanding of the meaning of, say, "おいしい食べ物" ('delicious food') -- 'edible things that are pleasant to the sense of taste' -- the set of things that actually fit that description varies somewhat from person to person. Anyone's list will be largely made up of things you do consider are indeed delicious foods, but it is bound to contain a few that you don't, and if you are not too sure about the meaning of the phrase, that can make you think twice.