have a try僅僅表示試壹下。
try again強調再次嘗試。
例句：
have a try
1、I will have a try even though I should fail.
哪怕失敗，我也要試壹下。
2、Let me have a try at it.
讓我試壹下。
3、You might as well have a try.; Why not have a try?
妳何妨試壹試。
try again
1、You might well try again.
妳無妨再試壹下。
2、All I can suggest is that you just hang fire and wait a minute or two and try again.
我的建議就是，先緩壹緩，等上壹兩分鐘再試壹次。
3、Why not try again?
為何不再試壹下？