How so, to try a fish??
Try meaning to taste for the first time, of course.
Please forgive the lame question.
You answered your own question, and it wasn't a lame one - have a lingot! :D
Why can't I use the verb προσπαθείσεις here?
Because προσπαθήσεις does mean try, but not in the sense os taste.
Πρέπει να προσπαθήσεις περισσότερο - You have to try harder.
Πρέπει να δοκιμάσεις το ψάρι - You have to try the fish.
Same verb in English, but two dofferent verbs in Greek. ^.^
I wrote "δοκιμαστεστε" instead, is this also correct (as the "you" in english is ambiguous)?
I'm not sure if this was your exact spelling, but it's wrong. Δοκιμάζετε is the coreect plural form that could be used here. ^.^
Oops yes sorry, I spelled that a bit weird. Glad to know the thought was correct though :)
Προσπαθείς το ψάρι
That doesn't make sense at all in Greek. When it comes to trying food, δοκιμάζω is the only proper word for it. Προσπαθώ is just translated as putting effort into doing sth. ^.^