Foundation for retaining wall on a hardcore base?
You need a good base for the wall to be stable so I would remove the hardcore and place the footing at least down to original compacted soil.

For the depth of the footing, if you mean the depth of the concrete, 225 mm is good. If you mean how far down in the soil, then either the depth of the footing (225 mm) or provide a decent sized width of footing on the soil retained side. There are two main items to address with the wall, overturning and sliding. The forces are minimal for a 800 mm tall wall assuming no surcharges and it's drained well so no hydrostatic loads. The sliding resistance has to come from somewhere. Some of it is soil friction. Some of it is resistance on the front of the footing from the soil. If the front of the footing is in hardcore then it will not provide much resistance. To increase friction you need weight. To get wait, you have the depth of soil on the retained side. Make the footing wider here by say 400 mm and this should be enough. This will also increase the resistance to overturning.

To get better numbers on sizes and what else to do would require doing a design.