The damage is likely caused by flea beetles. Flea beetles are shiny oval blue-black beetles, about 1/10 inch long. The larvae are tiny and gray in color. Flea beetles prefer hot and dry conditions. Flea beetles get their name from the quick hopping motion that they make when they are disturbed.
Adult flea beetles have an appetite for many garden vegetables, including tomato, potato, beet, chard, eggplant, pepper, and radish; they are also attracted to marigold and nasturtium.
Adult flea beetles chew leaves, leaving pits or small holes in the foliage. Older plants can withstand some damage; however, younger transplants may dry out and die from the many holes riddling their leaves. Jumping from plant to plant, flea beetles also spread diseases such as early blight and bacterial wilt; tomatoes are often a victim.
Adult flea beetles overwinter in weeds and garden debris, and may overwinter in nasturtium vines left standing in the garden. In late spring they lay tiny white eggs under the soil around the host plants. Larvae feed and pupate underground. There are one to four generations per year.
Preventing flea beetle infestations can be helped by cleaning up the garden to remove havens for overwintering adults. Because flea beetle eggs are deposited in the soil, frequent cultivation will cut down on the number of eggs, larvae and pupa in the soil. It is a good gardening practice to eliminate weeds in the garden area, as these insects thrive on them. To protect seedlings in the spring, use floating row covers. Keep garden beds well irrigated in the summer. Flea beetles shy away from shade. Plant vegetables close together and thin later when flea beetles are less of a threat. . Use mulch to keep the ground moist and less attractive to egg laying adults. Lightly misting the leaves of vegetables under siege may make foliage less attractive to flea beetles. You can kill adult beetles by spraying with an insecticidal soap. Wood ashes repel flea beetles, and can be used in two ways: either place a mixture of equal parts of ashes and agricultural lime in small containers around the plants, or simply sprinkle a spoonful of ashes on each plant two to three times per week. You can also repel the flea beetles with a spray made from garlic. Bulbs or whole garlic plants are minced in an electric blender with a cup of water, and the resulting brew is strained, diluted and sprayed on the plants. In a short time the flea beetles should be on their way.