I'm currently stuck at the Beast Man Lugar boss in the Moonlight forest. It seems like every time I use an item or spell, Lugar pulls off an 'attack all' move that deal 240-300 damage to all my party members. What makes it worse is that he'll use the attack twice in a row; killing all my party members before I can use any items.

My current party members are all level 23 and have the best items I can buy from the Moonlight Village:

Hawk: Ninja
Angela: Sorceress
Rise: Valkyrie

Am I missing something or is this a case of grinding my team's levels even more?

You should be fine. What you'll notice is that Lugar only goes completely mental with his attacks if you use a level 2 tech, an OFFENSIVE spell (Riesz's stat up spells don't count) or an item that specifically targets him, like a pumpkin bomb.

His counters will get progressively stronger as the fight goes on so what you want to do is set your allies to "Use level 1 techs only" and at the beginning of the fight, cast all your jutsus on him to lower his stats and all Riesz's stat up spells to increase your damage. He may counterattack but it will only be single target since it's early in the fight.

Then it is just a matter of beating on him with physical attacks and level one techs until he dies. If he does use his screen wide attacks then hammer the item button and with a little luck you should be able to use one just between his attacks.

Hope this helps.