That's just stupid. If the definitions in the drop-down are not acceptable (i.e. correct alternatives), they should not be included in the drop-down; and, DL should make an on-site dictionary easily available. Also, the first one is not always correct, And, frequently the first one does not make sense in the sentence.
That's always the case with dictionaries, especially if they do not provide examples to help you understand how a meaning is applied. This is simply a fact of life with these hints.
On the other hand, when you do check a definition via that mechanism, it signals to Duo that you don't have full command of its meaning and you will encounter more sentences with the word to translate. So, the true value may be training Duo to drill you where you need more exposure.
And they should try to resolve the tensions in the Middle East.
You know, there is a limit to how much can be accomplished behind the scenes of a free language learning program. If you find the "drop-down" hints/definitions to be misleading or of limited utility, you should stop using them as an infallible guide. Apparently, you will be better off.
To do that, I think that you'd either have to use 'salir', as AyoTa.SA suggested, or use 'irse'.
I'm not 100% sure on how to use 'irse' properly, so it would be great if someone could back me up or correct me, I can translate it just fine, but I sometimes struggle getting the words right myself as I am still learning.
Basically, as far as I understand it, 'ir' means 'to go', whereas 'irse' means 'to leave'. So in order for it to be "she can try to leave", I think that it would be "Ella se puede tratar de ir" (or ''Ella puede tratar de salir'' as AyoTa.SA said.)
Hotel California? Last lines of the classic Eagles song: "You can check-out any time you like, But you can never leave! " (http://www.azlyrics.com/lyrics/eagles/hotelcalifornia.html)
Spanish prepositions are difficult because there isn't always a one-for-one correspondence to English and a preposition can change the meaning of the verb it follows, which is the case here. "Tratar de" means "to try to." Take a look at the following link. Scroll down to "tratar de" and look at some of the others. Don't try to digest the whole page at once, but be sure to bookmark it to refer to it when you need it.
I don't think Duo was ever meant to be a stand-alone program. It needs to be supplemented by other resources: these discussions, a good dictionary, maybe a good grammar book, and the internet. There's a lot to learn. Keep at it!