With a stealth build, the Mogami has a 9.3 detection radius. Use that to your advantage on getting the jump on ships. Know when to hold your fire, don't be the first spotted (especially in a bottom tier match). If you note a lot of ships focusing you, then stop firing, assuming that you have nothing within range to detect you. If you are detected and fired upon, then use the ship's maneuverability to dodge the shells. For instance, you're sailing full speed broadside to a BB that has just launched a salvo at you from say, 18 km away. That's plenty of time to dodge for the Mogami. Immediately slow down and turn so that the shells land short of the ship. If you do get caught with a broadside, then pray it isn't a citadel (it will be though).
The transition from the Myoko to the Mogami is drastic. In the Myoko you can angle and tank the damage, Mogami... not against the ships you'll be going against (Yamato ;-;). Make the best use of your camo and agility, avoid that instinct to constantly sling HE at ships, only do so when you're confident you can avoid incoming fire. I only have 50~ games in the ship though, so I'm still getting the hang of it myself. :)