Disease on euonymus hedge
Foliar fungal diseases are very common on euonymus shrubs. Fungal diseases cannot be cured once the symptoms are widespread. And, while it is possible to prevent fungal diseases by spraying the shrub with a preventative fungicide, it is not practical for homeowners to engage in such a practice.
One way to help prevent fungal disease is to thin out the foliage and allow better air circulation, but this decreases the plants attractiveness.
You could simply prune out the affected areas and wait for new growth to emerge.