趣味 means “a hobby”. The particle で is used to explain the background or situation when the particular action or thing happens. So 趣味で means “as a hobby“ which explains why he is doing the following action.
ヒーロー means “a hero“.
を is the particle that indicates the direct object of the following action.
And the following action is やっている meaning “doing”, the present progressive tense of the verb “やる” meaning “to do”. There is another verb with the same meaning, which is する. Both やる and する have many idiomatic usages but when they simply mean “to do some volitional actions” they are interchangeable so he can also say ヒーローをしている. But やる sounds a bit more casual than する.
So ヒーローをやっている means “doing a hero”.
者 means “a person“, used towards yourself or someone with a lower status. When you want to modify a noun with a clause in English, you need a relative pronoun such as who, which, that, and so on. In Japanese you don’t need such things. All you need to do is to change the word order. For example, “the book (本) that I am reading (私が読んでいる)” is 私が読んでいる本, “things (物) that I ate this morning (今朝私が食べた)” is 今朝私が食べた物.
So 趣味でヒーローをやっている者 means “a person who is doing a hero as a hobby”.
Lastly, だ is the auxiliary verb attached to a noun or na-adjective to make the statement affirmative or declarative. So in this case it’s “I am”. The topic of this sentence “俺は” is omitted which often happens in Japanese.