While Railjack missions center around ship-to-ship fighting, you will need to get on board some enemy vessels to deal with them. Grineer Galleons are so large that there is no way your Railjack will be able to damage them. There isn’t even much you can do from the inside. To deal with these enormous threats, you will need to take out there commander.
You should try to get as close to them as you can manage in the Railjack, then jump out in Archwing mode. Carefully make your way to the waypoint; this is the entrance to the Galleon. You will need to dodge a lot of enemies here, so it can be best to do most of the other fighting first, and take out as many enemy fighters and Crewships as you can before going for the Galleon.
When you arrive at the entrance, hit “X” to enter. Once inside, the layout is the same as a standard Grineer mission, follow the waypoint to get to the commander, and kill them. Now that the job is done track the same route back to the spot you came in. Use your map if you need to do so as, at the moment, no waypoint will populate to show you how to get out.
When you get back, you need to be careful. Unlike a Crewship, where you just run to the very end and then hit “X” to leave, the spot you need to interact with to leave a Galleon is a little bit inside the ship, and quite easy to miss. Just pay close attention as you move down the hallway, and you will see it.
When you are back outside, you can make your way back to your Railjack, and help the rest of the crew to complete the mission.