Slowly approach him while shielding the arrows. (Don't shield if you're close enough for a grab though)
Short hop the arrows while approaching him. Make sure to NOT short hop when in range of any attack (including dash attack) unless you know you have a better lption than him.
Roll behind him. (Don't spam it or it eill become predictable and you will get punished. As a rule of thumb if you get punished twice for rolling try a different option for the rest of the match)
Jump and fall on him and either bait him into a laggy smash (then punish) or hit him with an option good enough to beat his.
Use one of your specific character's anti missile options. Reflectors, invulnerabilities (Zelda's Up-B), Super Armor (Donkey Kong's Up-B), High Priority Moves (Falcon Kick), etc. Use them effectively against spammers.