If you start your first playthrough on Hardcore, the difficulty actually will come naturally to you, like me.
The key here is to keep rolling/dodging around the base you want to capture. Use the grapple hook most of the time to get from one side of the base to another in a very short time. But first, before starting off, grab a helicopter nearby or right in the base if you want, and get rid of all the major structures first. Then, use the helicopter as much as you can to land near supplies and grab them, until it is finally shot down.
As long as you use my strategy of rolling/dodging all the time when moving around the base, most of the enemy's gunfire will miss you and you can even survive an outright assault for quite a while. Use dual guns to quickly mow down enemies. You will find this easier than you think, trust me. Have fun! =3