One common issue with larger cups in general, and with larger cups on smaller bands especially, is that the strap is positioned way to far out. That causes the fabric to cut into the arm, affects the fit, shape and support of the cup and causes the straps to slip down. If you have narrow shoulders the last one should definitly be familiar too you.
In this tutorial I will be assuming that you are doing this with a sewing machine. This is mainly for simplicity, most people don't know much about making durable elastic seams by hand, and because most people will be using one for this. You don't need anything fancy, just being able to sew zigzag is enough. You also need matching thread and a fresh sewing needle.
1. Take a look at what you have got
First, just look at the bra. See how the seams have been made, in what order. As the aim is to recreate this later, if this is the first time, work on one side at the time so the other one can be used as a reference. Here the strap have been attatched last, with two rows of very narrow zigzag. Before that the eleastic along the armhole have been sewn, with the top seam along the actual armhole first, then flipping it over and the second seam have been made. The elastic is in almost every bra sewn like this, apart from some Freya bras that actually only have one seam. After taking a close look, rip all of these seams. The top one at the armhole you might want to leave a cm or two off as it is harder to reattach it that close to the underwire.