You keep party level and get to pick some items and equipment to take with you onto the next playthrough, while everything else is reset for the most part (including quests)

I was Lv.80 Shulk, Lv.79 Reyn, and Lv.79 with Sharla. It help to have advanced healing spells so as to heal more often and in larger doses. As far as strategy goes, I just hit Zanza with Monado Buster and backslash until he's K.O'd and to save up chain atk for reviving party members and having the AI revive Shulk because chances are he'll be Zanza's target if your using backslash alot. On 1st and 2nd form takeout Zanza's minions or at least one because I think he doesn't respawn them if there is still one on the battlefield.. Just make sure your party can withstand the extra dmg. Took me about a dozen times to kill Zanza but keep at it and eventually you'll get to 3rd form which is a breeze compared to the first two forms.

I hope this helps!