For the maximum rating possible on a quest you're going to need three things - planning, practice and luck.
Don't forget that you can use gold and stat-enhancing trophies to bypass a lot of poor luck.
The closer you go into the center of the board, the more challenging the encounters you'll face.
Knowing when to make a move inwards is largely a question of practise (understand the objects and followers at hand), and also the specific requirements of the quest you're on. Don't try to head into the center of the board too early unless the strength of your character and followers allows for it.
Don't forget to cash in your trophies when you have a decent selection as these can make a serious difference to your attacking power.
Don't use up your Fate re-roll unless it's absolutely necessary - to prevent a complete loss of all lives for example.
Psychic Combat is similar to the traditional Strength-based combat but it differs in two very simple but important areas. For these battles, your ability to fight is determined by your Craft level instead of your Strength attribute. In addition, any objects you have in your possession that would normally mitigate a death become invalid during combat. This is one occasion where it's worth keeping your Fate re-roll in mind.
Be aware that when you make a crossing into the Inner Region of the board, no dice-roll occurs and you will only be able to move one square at a time. Creatures living inside the Inner Region are also immune to spells, and you can't evade fighting them either. Enter the center of the board at your peril, and make sure you're prepared!