'试试'can be translated into 'have a try',just a process,and the actor doesn't mind whether the result is ok or bad.sometimes the actor just consider it as a game.例如:你能举起150公斤重的杠铃吗?我试试。不在乎能不能成功。
'尝试'='try one's best',when someone use '尝试'to do something,indicates the actor do something with a hope to be successful.and he has made adequate preparation.例如:姚明在休养了6个月后,开始尝试进行恢复性训练。希望能够成功。