The item requirements for skill quests involve items with guaranteed drop rates. It is recommended to do these quests in a party as it is easier, takes less time, and consumes less stamina. In order to unlock a Locked Skill, you need to complete a series of quests for each skill. Normally, you cannot upgrade nor obtain that certain skill.
You will notice several skills with a padlock symbol on it. Skill Quests can be obtained from Camilla or the Board.