I would forget Eagle. They have a rep here for being picky to the point of absurdity. You are going to have to selectively target some others. A lot of them will not touch a DUI. I would think they have the common sense to see a reformation pattern if you straighten up for some number of years, say 3 minimum, but with all the apps clogging the typical regional inbox you will still be lucky to get an interview. Use the search engine on the upper lefthand side and google previous threads on Eagle, there's lots of previous threads here. Here's one. You will get fly if you stick with it, but that rough start will have to be overcome. There's currently no pilot shortage and lots of perfect applicants.
Am I doomed?