It might take a few attempts, but this is an easy way past the only boss fight in Dark Souls III that doesn't give you the option to level up beforehand. Try to keep yourself a medium distance from the boss get too close and he'll rock you with melee attacks, but get too far away and he'll close the distance with punishing leap attacks. Just hammer him with fireballs - rolling to dodge attacks all the while - until he's gone. Two full FP bars is all you need to take out the tutorial boss.

Estus Flasks still heal you in Dark Souls III the 'Ashen' variant recharges your Focus Points (FP), which are spent every time you cast a spell.

First you need to thoroughly explore the area leading up to the boss, to find the Ashen Estus Flask.