Always invest in Lupo's maps when you have the opportunity. This NPC who is a cartographer sells a map of whichever region you are in for several hundred Spirit Light orbs which will not only give you a full outline of the region and collectibles within it but tells you where to explore next for upgrades.
Do Baur's Reach First
After a few hours of gameplay you will be given the option to tackle three areas - Baur's Reach, Luma Pools, and Mouldwood Depths in whatever order you want. Select Baur's Reach first as doing so will enable you to unlock an ability called Light Burst which you will help you out a lot in Luma Pools. The area you should save until last is Mouldwood Depths as spiders live there.
Get the Spirit Smash Ability
Once you have acquired your basic melee attack you will be able to purchase one ability at a discounted price. Make sure that the ability you choose is Spirit Smash as you will need this hammer of light to deal heavy damage against enemies and crack open secret walls.
Get the Triple-Jump Spirit Shard
Not long after you have your first ability you will meet a merchant who sells Spirit Shards. The one you should purchase is triple-jump as it will enable you to clear sections of the game considerably easier an allow you to access several areas and secrets early.
Use Different Abilities
Unlike the first game in the series Ori is now able to equip various abilities. Ori starts of with Spirit Edge (a sword) and Spirit Arc (a bow). As you earn more Spirit Light, you can unlock Spirit Star (a boomerang), Spike (a spear), and Spirit Smash (a hammer/mace) by talking to Opher the merchant. Becoming familiar with all of these different abilities will improve your chances in combat shrines.