Some of the skills that do not say "Area" may be an area attack the games website doesn't have all the correct information but i did my best to fix the ones i know are an area attack.
lvl 0 Flame Arrow
lvl 5 Flaming Spear
lvl 10 Produce Ice
lvl 15 Fireball
lvl 20 Fire Burst - Buff and Produce Flame - Area
lvl 25 Spike Ice Arrow
lvl 30 Cloud Kill and Fire Pierce - Area
lvl 35 ice Sword and Chill Touch
lvl 40 Dual Flame Arrow and Fire Wall - Area
lvl 45 Flaming Corum
lvl 50 Produce Ice Arrow
lvl 55 Dark Fireball
lvl 60 Dark Produce Flame and Dark Fire Chant - Buff
lvl 65 Spike Ice Wave - Area
lvl 70 Death Fog and Dark Fire Pierce - Area
lvl 75 Ice Sword Corum and Hell Scream
lvl 80 Triple Flame Arrow and Dark Fire Corum - Area
lvl 85 Strike Corum
lvl 90 Produce Iceberg
lvl 95 Death Fireball
lvl 100 Death Produce Flame and Death Fire Aura - Buff
lvl 105 Spike Ice Meteor - Area
lvl 110 Death Fire Pierce - Area and Death Fog Kill - Area
lvl 115 Collapse and Ice Sword Hell - Area
lvl 120 Death Fire Corum - Area