Ivy has a very tough leaf and stem and it is difficult to achieve absorption and uptake of the weedkiller by this plant. The best products to use are Roundup or Roundup Tough Weedkiller.
Treat new, young growth where possible as this will be more vulnerable and gently bruising the leaves before application by walking amongst it or brushing the leaves with a stiff brush, will aid uptake of the weedkiller. After spraying, do not be tempted to remove the top growth until it has fully died back. Apply the product efficiently and repeat at approximately 4-week intervals until the area is clear.
Additional advice is to cut back and pull away as much growth as possible to reduce the problem. Unfortunately once this type of growth gets established it can be very invasive and difficult to control.