Fast and hard way to improve your corsair reputation
At the beginning corsairs hated me, 2 hours later they were almost friendly (3 and half positive blocks).
I went to Omega 11, there is a Red Hessians base there, just dock at Solaris base and then navigate slowly towards the Hessians base you'll be attacked by waves of level 12-14 stilettos. Killing one of those fighters will improve your corsair rep about 1/10 of block, moreover they'll drop level 8 weapons that sell really good.
Just be careful, the sun there needs to be respected, if you go too near you'll melt like an ice cream.
I went to Omega 11, there is a Red Hessians base there, just dock at Solaris base and then navigate slowly towards the Hessians base you'll be attacked by waves of level 12-14 stilettos. Killing one of those fighters will improve your corsair rep about 1/10 of block, moreover they'll drop level 8 weapons that sell really good.
Just be careful, the sun there needs to be respected, if you go too near you'll melt like an ice cream.