First of all, you can buy dynamite in Neevah on Arean Island, and Rope in Hesterville, on Haine.
Pepp Valley: Secret passage to the right through the trees on lower path.
Alavon Forest: I believe I recently helped you with this one; secret passage through the trees to the lower-right of the central area with the four towers.
Winstar Forest: You have to get to this one from Mt. Gareth. From the entrance, enter the cave on the left, and in the next area, enter the left cave again. In this cave, take the left exit to find a golden post. Use rope to reach the path that leads to the spring back in the forest.
Fiyara Forest (the one with pink trees): In the area before the desert, there's a secret passage in the trees to the right.
Glymac Forest: Secret passage from mines (big switch track area); need dynamite.
Haine Wilds: In the area off the coast, you need rope to scale cliff, then you need Maximus to cut down the tree and make a log bridge.
Mesomia Forest: From the center island with the four bridges, take the lower-right bridge and use the raft; choose to go to the left.
Hobo Island: When you first enter the beach area to the east of the village, you should see a little bit of land out in the water. Just above the first large, flat rock you come to, there is a secret path you can follow in the water; follow it all the way to the right to reach the spring. Also, you can go down at the end and find some Spicy Herbs to take back to Pepp so the Goth Lord can make Neo Tonic; these herbs are hidden all over Hobo Island.
Cambria Island: After landing here with Vulcan, proceed west through the first area. You then come to a lake. Go north, and at the end of this area there's a cracked rock wall where you can use dynamite to uncover the spring.
Islan Island: When you cross the tundra and enter the frozen forest, keep going south and follow the path to a frozen lake. You'll have to melt a couple of ice towers (make sure Leonardo has full EF). The spring is on an island in the middle of the lake.
Behgar Island (South): Exit Fauston (the village of white-robed mystics) to the east, and go into the woods; there is a network of secret passages in the trees you'll have to navigate to reach this spring.
Shady Islet: Once you learn about the Shady Islet (near the end of your quest on Behgar Island), go there with Vulcan. There is a secret passage through the trees to the left of the landing area where you'll find the spring.