How to attack enemy tiles (red tiles in eden) with cavalry and with just one hit?

To take a tile in 1 hit you need a legion with a demolition power of 500+. Most cavalry legions max out below 500, but this can be increased in 2 ways.

The cavalry hero 'The Avalanche' has a skill that boosts demo power. She is an X hero but if you can recruit and use her it will be easy.

In your Specialty options you can unlock skills in the Blue section upwards that increase demo power. If you have enough points to spare for these then you can increase all legions demolition with this method.