For The Dry Spell achievement you need to have a furnace, fuel, water and a sponge. You should already have all the items except the sponge. (if you already have a sponge just make it soak up some water and put it in the furnace ;))
Assuming you don't have sponge yet you should start looking for Ocean Monuments, they generally have a room containing a few sponges. Ocean Monuments are naturally generated so if you're having a hard time finding one use this website: http://chunkbase.com/apps/ocean-monument-finder
I have never used this before but if you enter your seed and select Xbox One/PS4 below the map it should work.
Once you've found a sponge just let it soak up some water in nearby river/lake and put it in the furnace with whatever fuel you have at hand and you knocked out another Minecraft Achievement.Current Tutorial World method (Thanks to Awoo)
Coordinates (Thanks to DaigleTheBagel
Don't forget to bring the materials needed to complete the achievement!
x = -397
y = 92
z = -95
There's a sponge in a chest halfway up one of the watchtowers on the west coast of the current tutorial world. The fastest way to get there is by using the Elytra in the chest and jump off the tower facing west. Just keep going until you reach the ocean, then look around for the tower. If you run into the giant Wither statue, it's a bit south of that. The chest is in a little hut inside the tower, bring a few blocks so you can climb up there.