The following video will show you ALL 13 Royal Arms locations to unlock the Faithful Heir Trophy. Each Royal Arm has unique attack patterns and stat boosts and can be used in combat by Noctis.
Watch the video #1 - Sword of the Wise - 0:05
#2 - Axe of the Conqueror - 0:58
#3 - Swords of the Wanderer - 2:08
#4 - Blade of the Mystic - 3:26
#5 - Katana of the Warrior - 4:13
#6 - Trident of the Oracle - 5:29
#7 - Sword of the Father - 6:21
#8 - Bow of the Clever - 7:20
#9 - Sword of the Tall - 9:39
#10 - Shield of the Just - 12:09
#11 - Scepter of the Pious - 13:27