Going to need photos Bessie. From my own personal experience I have grown Shasta Daisies for many years and have not had anything munching on them six, four or two legged. So I find this an interesting problem. It could be a pest that has no legs at all though and that is slugs. A good photo showing the damage to your plant could reveal if it is a slug since they have scraping mouthparts the markings of which is quite evident on a leaf. I have many frogs in my garden so my Shasta's are free of that possibility too

We have had to give up trying the new varieties of these. Every one we have planted has been eaten away to nothing by snails within 24 hours of planting. Strangely the old fashioned Wirral Supreme is totally unaffected by the molluscs. Would love to have Broadway Lights or any of the other yellow ones, but no chance.
And we have hundreds of frogs and nets in the garden which are supposed to eat the molluscs.

Slugs or snails. Mine was eaten to the ground overnight by the day after I planted it. No point trying again.

I had the same problem Bessie. slugs/snails were the culprit.
welcome to GoY