More than likely, flea beetles are causing the holes in the radish leaves. They are called flea beetles because they hop around like fleas but are not related to fleas. They like radishes, kale, broccoli and all of the Brassica family.
They look like little black dots and when the leaves are disturbed they bounce away. Yellow sticky cards and be placed around the radishes on holders up above ground to trap the insects when they jump. The flea beetles are attracted to yellow.

 Disturbing the soil around the radishes will kill any larva that may be present. Organic Neem oil can be sprayed on both sides of the leaves. Neem oil will kill any insect it comes in contact with but won't harm the plants. It lasts about 3 days and anything that eats the plant will ingest the Neem oil and die.

Flea beetles generally don't do much harm to radishes other than cosmetic damage to the leaves.

A website about growing radishes is listed below.

https://extension.umn.edu/vegetables/growing-radishes

Don't be too concerned about the holes in the radish leaves.  The radishes should continue to grow and be ready for harvest soon.