I believe you. Moles can be quite destructive to a variety of plantings.

If the flower beds are "raised" lining the beds with 1/4" hard cloth will work. If the flowers are simply planted in the ground, the hard cloth can work but it is more tedious to work with as you would need to cut the material around existing bushes and trees.

Exclusion is generally considered the best approach to minimizing mole digging damage as most (if not all) toxic mole baits are not effective, and trapping of moles can be quite difficult.

If you choose to try and trap, I suggest you try the "cinch" trap as people seem to have the best luck with that model. I'm sure you can find a distributor on-line.