[Michael]

Go for it! – said when a great opportunity comes up, e.g. a chance to lead an
important presentation for your company

Do your best! – said to someone who faces a difficult challenge, e.g. when someone
wants to win a karaoke contest

Hang in there! – said to someone in a difficult situation who needs great strength,
patience or endurance e.g. a person half-way through a marathon who
wants to quit

I hope this helps!

[kanata08]

物事の難易度としては
hang in there>do your best>go for it　の順でしょうか。
熟語帳を見ても違いが分からなかったので助かりました。

johnstmich先生、回答ありがとうございました。

[Gerard]

Go for it! DO your best! Hang in there! are all positive exhortations meant to lift the spirits of the person being spoken to, the Japanese equivalent being “Gambattemasu!”

[Nizza]

Go for it and Do your best are the words to lift or to cheer up someone! For example, if you have a test or in a simple soccer game!you can say, Go for it! Do your best! Gambatte!