The moon lord in expert mode is somewhat tricky but there are a few things to note for expert mode, under any circumstance do not use rod of discord, one or two extra ports here and there will render you dead in a matter of seconds. Firstly I highly recommend using a yo-yo, either The eye of Cthulhu or Terrarian combined with the master yo-yo bag which can essentially double your dps.
I am going to jump and assume you are using melee and in which case I strongly suggest all your accessories to be warding, when it comes to accessories there are 3 items I do not live without when it comes to bosses, Turtle shell, Shiny Stone and Star vail necklace. The yo-yo bag replaces my ankh shield and flesh knuckles replace my celestial stone (gives more def). Mount I used cosmic car but fishron mount with periodic water bubbles gives you insane speed to keep ahead of the moon lord.
Now for tactics, keep ahead of the moon lord is key as well as moving in a wave up and down to best avoid eye summons. As annoying as this may sound, deliberately not fighting the lord could help you out (hear me out) Im kind of an odd person, my specialty is numbers and what I did was summon and watch the moon lords attacks, the time from when his eye closes to when it opens again can save your life. Doing so and being able to predict the laser fire and do a sweep over his head to avoid damage is the best way (not rod of discord or going under, best is going over). This also lets you target the hands somewhat evenly and easily.
His grapple can be killed and if so leaves a gap where you will take damage if you cross it which again sweeping over his head avoids this. Lastly, bring every kind of buff possible though this does mean you need to have both crimson and corruption but that is easily done. Good luck.