I think the easiest way to deal with them is to use weapons that decrease their attack so they can't hit you, like EMPs or the Power Virus can stack 3 times. As long as your defense is reasonable they shouldn't be able to hit you much having their attack dropped.
I'd also suggest investing in item crafting if you can afford it. My ship that I just got to level 40 has over 5,000 shields, mostly from using the Utopian's ability, because the item's stats will increase as you add slots to the item. Shields are fairly cheap to improve, and starting with the two dot yellow items seems to give the most return for the expense.
Defense is a great stat to boost up as well, usually from a good drive and computer I'll have less than a 40% chance to be hit.
If you don't know, equipping items that are better than your base stat is kind of critical in this game, like putting in all the crew that boost helm, plus a few crew equipment items and you'll be able to equip a better drive, then remove all the stuff and your drive will still function the same.