Bowbly, the initial founder of what we now call attachment, said there were only two ways to go from insecure to secure attachment and he also said it would not be necessarily complete for all relationships or even a primary one.

The two were a long term intimate relationship (implicitly a healthy one) and intensive psychotherapy. He didn't say you had to have both.

I have had both. I had an insecure attachment style that would have been called avoidant or in adult terms dismissive, which means that when I was distressed as a child I didn't seek out comfort because in my case no one would have provided it. So I developed a premature independence, or at least the appearance of that. Avoidant/dismissive does not mean you do not want an attachment; you do, but it means that there is something blocking the way, usually fear which in my case was caused by abandonment and neglect.

In therapy I worked this through in the transference/countertransference dance, where attachment needs were reactivated and I was able to do reparative work. This took time and lots of patience, but apparently it is possible to become securely attached even with a difficult background.

In moments of distress, I do now seek out comfort and am able to trust. I had to make friends with all sorts of emotions that I had blocked off, but that actually felt good to do after getting used to it. I also had to be gentle with myself when I went through needy periods, which tended to be in relation to my therapist not to others.

I do believe it can be done. And many therapy approaches use attachment and attachment repair as part of the treatment. It is one of the more validated aspects of what came out of a psychoanalytic context.