Those three are different expressions with little in common.
* -아/어 보다 = try doing something (to see what happens). It's a general phrase not tied to a particular tense.
* -(은)ㄴ 적이 있다 = have done something (적 = time, experience). This is a fixed tense (present perfect) expression.
* -(은)ㄴ 일이 있다 = have a certain matter/issue (일 = specific matter). Usually used in the present or past tense.
Examples:
* 도전해 봐. 해 봐야 성공할 수 있어 = Give it a shot. You can only succeed by trying it.
* 너무 힘들면 과장님한테 말해 봐 = Try and talk to your manager if it's too difficult for you.
* 나는 팔이 부러졌던 적이 한 번 있다 = I've had my arm broken once.
* 너 일본에 가 본 적이 있니? = Have you ever been to Japan?
* 친구는 요즘 힘든 일이 있다고 했다 = My friend said he had a difficult problem lately.
* 무슨 일(이) 있으세요? 아니요, 아무 일도 없어요 = Is anything the matter? No, nothing's the matter.