Always stop to collect any Amenoculus you see floating nearby. These collectibles can be traded into the Statue of the Seven scattered around the world to level it up. Doing so gives you a bunch of rewards, including more stamina so you can climb higher or paraglide for longer.
Complete all the mini objectives in your Adventurer Handbook. It gives you a ton of resources and helps ensure you're not forgetting about some crucial progression system. If you're lost and unsure of what to do, this is always a great place to look.
A character who uses the greatsword will break rocks way quicker. If you're going to go mining, bringing a greatsword-wielding party member will help a lot. Failing that, Amber's Explosive Puppet ability will destroy most ore veins almost instantly.
Level your entire party evenly. Dungeons have level restrictions based on the average level of your party.