Make sure you stock up on cheap ingredients at each town you visit and practice cooking with different characters to discover new recipes. Different recipes can give you different benefits, these include health and stat increases.
Defending Against Enemies
Pay attention to the enemy types by keeping an eye out for their 'tells' or movements that indicate they are about to strike. Being able to put up your guard or back off at the right time can be the difference between a win and a 'Game Over', especially in boss fights. Practice using the Y guard button and remember that it can also be used to 'recover' mid-air if an attack throws you up high.
Don't Sell Old Weapons
Although you can always sell old weapons it is advised that you hold onto them because once the synthesis option becomes available you will be able to use it to craft new and better pieces of gear from bits you've obtained from monsters and old weapons.
Sorcerer's Ring
Once you have the Sorcerer's ring in your possession you will be able to begin solving puzzles and finding more treasure. Use the Sorcerer's Ring on anything that looks suspicious to make sure you find all the hidden chests.
Special Weapons
You may need to backtrack in sidequests if you want to get special equipment such as the Devils Arms weapons. Keep an eye out for anything unusual in dungeon that you are unable to access and make a note of it's location as there is a good chance you will be returning there later in a sidequest.
The Wonder Chef
Whenever you enter a new town be on the look-out for unusual items that may signal the appearance of the Wonder Chief. Every time you discover him he will give you a new recipe and ingredients.
Always Cook...