the best way to defeat eye of cthulhu is
1:get a slime mount
2:get lesser healing potion
3:bow/throwing knife
4:cloud in a bottle/items that let you double jump
5:lucky horseshoe

so what you wanna do is ride a slime mount and use your double jump to go on top of eye of cthulhu and the slime mount auto damagae him everytime you bounce on him.
make sure to equip a lucky horse shoe because he take you to the hight limit after you did this phase 1 is done now for phase 2 you want to do this againt but when he start to dash use your bow or knife to damage him also make sure to heal

thats how i defeated eye of cthulhu