As soon as you get the Aqua Boots, you are able to explore any screen on the map. Normally, Crawky Forest opens up when you defeat Warlic, but if you go back to the Warrior's grave where you found the Valley Sword in the Graveyard of Bachular, you can now follow the river west to Haidee's Forest. Rio will immediately warn you that the area is dangerous without the Legendary Sword, and she's right—this is, after all, the final area of the game. However, you can backtrack to Crawky Forest and get the Legendary Sword, among other things.
While the Aqua Boots allow you to explore freely, there are many caves that you will need the Ring of Invisibility to open. For that reason, it is wise to head to Fosbus' Swamp and pick it up before heading to the final areas. You'll also want to pick up as many Bibles as possible before making the trek—the Legendary Sword costs a massive 50,000 gold. You'll need to have purchased at least 14 Bibles in order to afford it.
The advantages of going to other areas out of order like this are questionable. It's certainly fun, but all you really gain is more money when you defeat early bosses (not to mention an easier time with those bosses). Since bosses are perhaps your best source of income, it may not be much of an advantage to save up and buy everything before fighting them.
If you do go exploring, your best bet is to head southwest from the lake you first enter, following the river south and then west until you reach Crawky Forest. Pick up items and upgrades there, and work your way back to Haidee's Forest when you are better equipped. Of course, actually defeating Warlic will make travel much easier, since doing so connects Crawky Forest to Warlic's Lake, so doing so might also be prudent. (Of course, then you're not really abusing the Aqua Boots anymore.)