What you need is translation from Japanese to English, right?
i'll try my luck - undameshi o yatte miyo
-I assume the Japanese sentence should be "....yatte miyou". (Last vowel is long.) It may be "Let's try our luck" or "I'll try my luck."
i was merely joking- tada jyodan o ittano da
-Correct.
i tried hard but to no avail- hone o otta ga dame datta
-Correct.
it's up to you - kimi no kangae shidai
-Correct.
it is pretty tough - sore wa ochigai
-Means "It's completely wrong."
it is beyond my power- boku no chikara dewa dekinai
-Correct.
he will come to his senses- kangae naosu daro
-Correct. The subject may be he or she.
he is a hopeless case- ano otoko wa dame da
-Correct.
he is smarter than he looks - mita tokoro yori riko da
-Correct. The subject may be he or she or you.
he shows off - ano hito wa ibaru
-Means "That person behaves arrogantly." "That person behaves as if he/she was superior than others."
he has a warm heart - nasako bukai hito da
-Correct. It should be "nasake bukai hito da". Otherwise it doesn't make sense.
he took the matter to the heart - kare wa sono ken o shindaishita
-"Shindaishita" doesn't make sense. Isn't it "shinpaishita" ?
If so, it means "he worried about the matter."
that is his forte - sore wa ano hito no ohako desu
-Correct.