“一次通过司法考试”英文怎么说？？

可以啊，你翻译的不错，不过将first改成one可能会更好。
"通过"也可以用success，翻译成succeed at the National Judicature Examination at one shot

at first shot 不错嘛

at one go 也行

Pass the National Judicature Examination at one blow.

at one blow:一次取得成功

这才是地道的

at a stretch

一口气地

专四写作文我就用了这个。。。

passed...at the first attempt.

or "at the first time" 这个很保险了

Pass the National Judicature Examination at the first time.