DESCRIPTION
This is very difficult to spot until it is too late, so prevention is better than cure,

The plants will look unhealthy but with no obvious signs of leaf damage. Growth will be stunted. 

If the soil is lightly turned over, you may well see the grey caterpillars of the Swift Moth in the soil feeding on the roots.

TREATMENT
Prevention is the only practical action. First, don't plant beetroot in the same soil two years running. Second, make sure the area is weed free - the caterpillars feed on the roots of some weeds, especially docks, and these only encourage them. 

If an attack does strike, destroy the affected plants by burning them. Dig the soil surface to expose the caterpillars to birds.