Bonum animum habere means "to have good courage, to be confident." This expression is used, for example, in the plays of Plautus.
I think you are somewhat mistaken when you characterize (in the comments) Thetis' words as "motivating her son." She suggests he only has the choice between ignominy and early death, which is a bleak outlook. In that context it makes perfect sense that he would in his response try to cheer her up.
Thus I think your objections to the second person imperative should be alleviated. Habe is the second person singular active imperative and fits well in this context.
You will indeed find this usage in Plautus, e.g.:
Tace, bonum habe animum, Euclio.
No doubt the authors of your exercise had that in mind. Otherwise, you could also say bono animo sis.
As a side note, Thetis was undisputably a very beautiful woman/nymph, but beatus, -a, -um does not mean "beautiful."