Leafminers aren’t susceptible to sprays working because most of the time the larvae are in their protective coverings.
Instead, removing the egg clusters, diseased leaves and nearby dock or lamb’s quarters. These plants are known to be a host for beet leafminers.
Additionally, attracting parasitic wasps is very helpful. This can be done by planting nectar plants. A good source for natural parasitic wasp is http://www.gardensalive.com
If spray is necessary use NEEM or avermectins.
Source: Rodale – Organic Gardening Handbook of Natural Insect and Control