Proud of it and even mentions the movie and Milius in his political life. He very often uses something Milius told him: "Pain is temporal, but the movie is eternal" or something like that.
Also check out his:https://conancompletist.forumactif.com/conan-the-barbarian-f3/arnold-using-his-sword-one-more-time-t1388.htm
I think he knows it was his best acting role ever. Watch the DVD with the audiocommentary, also.
Apparently he isn't ashamed of THE DESTROYER that much, maybe for commercial reasons because even though the movie was awful, it was his second major role and that very same year he did TERMINATOR so his career was going pretty well. Tough in the DVD of CTB he tells Milius "i'm still waiting for you to make the second one", like he knows THE DESTROYER was bad... But it's really Milius who hates THE DESTROYER more than Arnold.
The one Arnold really hates is RED SONJA, but I think his work there is less bad than in THE DESTROYER... But he hates that movie mostly because he was kinda forced to do it, and plus he was a secondary character... But I really believe Arnold has made much worse movies than RED SONJA.