Ivy is difficult to remove as it roots where the stems touch the soil. However in a planter box it should not be such a daunting task. Cut back the growth to where you can see what you are doing and pull out any shallowly rooted pieces. Then dig out the larger plants. If this is not possible, you can cut the stems close to the ground and then apply glyphosate (Round Up) carefully to the cut stems. The herbicide will be taken down to the roots which will then die and the plants can be removed. It may take a little time for this to happen, so be patient and plant annuals for color over the dying ivy. Round Up breaks down in the soil within a few weeks so follow the instructins and don't plant the annuals too soon.