How do you take purple tiles with only one attack?

Tiles have a durability of 500. You need to make a legion march with a demolition (destruction) power of at least 500 to take it in one hit. You can see the demolition power in the legions list on the top left of each.

In general the only way to get above 500 is to use Footmen. They have the highest value. The more troops and the higher tier the better. There are also research items to boost this.