For the 1888 half penny there are six die varieties consisting of five obverse dies paired with two reverse dies.  Differences can be located by checking for repunched letters and comparing the alignment of the letters of BRITANNIAR.  For the reverse dies there are differences in the spacing in the date.

Half Penny

The spacing is measured between the eights.

Obverse Dies:  BRITANNIAR

Well aligned BRITANNIAR

Well aligned BRITANNIAR;
Repunched first R

Misaligned BRITANNIAR;
High I and Low T

Obverse Dies:  Victoria

Clear letters

Crooked V in Victoria

Die Crack in Victoria

Repunched R in Victoria

Reverse Dies:
The Date

Wide 88

Narrow 88