Other than using Heal Orbs to cure yourself, the only other way to no longer be scared is to use the Omamori which will help remind you of just how awesome you are, and will steady your nerves & breathing.
As a Status Effect, this one's effectiveness depends on your strength compared to your target. If your trying a new boss for the first time and are unsure of if you'll win. Better safe than sorry and you should cure it. If your just farming areas, or doing Bounty Quests, you can use your own judgment on if you can ignore it or not.
The following locations, enemies, and bosses can cause you to become Scared.
- Training Dojo: Bushes(#6 on the map)
- Orc Camp: Crow Mountain Tunnel(#2 on the map), Windy Passageway(#13 on the map)
- Cavern of Ancient Ruins: Worn out Tunnel(#1 on the map)
- Cursed Forest: Corrosive Roots(#13 on the map)
- Mage Tower: Sky Bridge(#11 on the map)
- Flaming Volcano: Erupting Crust(#2 on the map), Vent(#13)
- Polar Glacier: Icebrick Stand(#13 on the map)
- Imperial Tomb: Lobby of Undead(#2 on the map), Pool of Blood(#10), Bone Knight(Enemy), Soul Gatherer(Enemy)
- Canyon of Immortality: Canyon Tunnel(#14 on the map), Soul Gatherer(Enemy)
- Dragon Archipelago: Water Slide(#11 on the map), Bahamut(3rd Boss)
- Abyssal Sea: Dead Sea(#2 on the map), West Sea Phenomenon(#5), Tsunami(#12), Siren(Enemey), Abyssal Nightmare(3rd Boss)
- Impact Site: Evolution Nidus(#16 on the map), Grandmother(1st Boss)
- Hellgate: Tunnel of Exile(#2 on the map), Slaughterhouse(#6), Hillock of Seduction(#8), Acheron's Fall((#10), Arch Demon(Enemy)
- Skyland: Angel Path(#1 on the map), Sky Falls(#5), Floating Rock(#12), Valkyrie
- Pandemonium: Path of Soul Imprisonment(#10 on the map), The End Road(#14), Grudge Beast(Enemy)