You can break a karmic cycle by healing the lesson it’s trying to teach you. You do this by cutting the cord to the habits and people associated with the karmic cycle, as your attachment to them keeps you in the cycle. This can be easier said than done, as karmic cycles are typically things of comfort and codependency.
Karmic cycles can sometimes manifest as attachments to addictions, mentalities, relationships, and places. They are pain points that are meant to make you hit rock bottom so you can change your way of being and move upwards. Having a spiritual practice can help bring you clarity on what it is that is no longer serving you.