Can I move twice and attack?

Yes and no...

If you move twice during your move phase you skip your main phase and go straight to your end phase. The moment your end phase ends, you exhaust the champion or summon who was active. However, at the beginning of the end phase, you can play any abilities you want that are swift speed.

Most attack abilities are swift speed, with the exception being Heavy Attacks, which are always action speed. So, yes, you can use any swift speed attack ability you want after moving twice - as long as you can pay the cost for it.