Really? When there is an enemy surface fleet sitting offshore supporting a landing, you can attack the surface fleet? How? Every time I try it doesn't work.
I do nothing special compared to any other regular surface fleet. I use a task force set to patrol in the sea zone(s) off the coast of the naval landing, for spotting, and a task force set to strike parked in a port nearby. Once the enemy surface fleet is spotted, the strike force comes out to engage and boom (assuming it thinks it can beat the enemy fleet based on engagement rule). I also add a sprinkling of naval bombers for extra punch when possible.
It works very well for me. In fact when playing as the UK or US, this is how I sink the bulk of the IJN as it seems the Japan AI player assigns most of its surface fleets to naval invasion support, and then proceeds to invade the Pacific islands...
I never move my strike fleet manually to attack. I don't know from experience, but others often report it doesn't work or it's unreliable.
I don't have MtG by the way, but I don't think it matters here.