書法比賽的英文

The following sentences may be better:
The most exciting moment I have had is winning the (English/ Chinese) penmanship competition in Primary six.
The happiest moment I have had is winning the (English/Chinese) penmanship compeition in Primary six.
One of the most exciting moments I have had is winning the (English/ Chinese) penmanship competition in Primary six.

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It should be penmanship competition.

The definition of penmanship : 書法
competition : 比賽


Thus, it will be "penmanship competition"

Calligraphy competition.
In my personal opinion, calligraphy is more like the art of writing (書法), and permanship means 字體 in general.

penmanship competition