やってみる The most broad meaning. I’ll try some lime ice cream. Let’s try flamenco dancing. If it doesn’t work out, whatever, we’re just killing some time here.   KIDS$$$
みる(こころみる) To attempt a difficult thing. Unlike やってみる、 you have a lot invested in whatever you are trying, and it tests the limits of your capabilities and/or tenacity.
(ためす) Usually means to test out a thing. “can I try it before I buy it?” “He tested his serum on animals first.” Etc.