It's a three stage building with a bit of crafting at each stage, so let's see what we're going to have to do...
[Please note, mission crafting is on the individual mission pages HERE. This is only the crafting for the Fountain itself.]
Stage One
8 Hole Augers - Requested
10 Granite Blocks - Drop from Rocks
8 Brick Mortar - Requested or Adult Pigs
2 Glass Lamps - Crafted
Each Glass Lamp needs 5 Iron Lamp Posts (Steel and Brass Forges) and 3 Frosted Glass (Requested).
Stage Two
12 Work Towels - Requested
8 Grip Wrenches - Requested
5 White Topiaries - Crafted
8 Iron Washers - Requested
8 Brick Mortar - Tending Adult Pigs
5 Fountain Pipes - Crafted
Each Topiary requires 5 Unruly Shrubs (Found tending Fresh Grass) and 3 Hedge Trimmers (Requested)
Each Fountain Pipe requires 5 Iron Bars (drops from Brass and Steel Forges) and 5 Pipe Forms (Requested)
Stage Three
10 Work Towels - Requested
8 Hedge Trimmers - Requested
2 Lion Statues - Crafted
10 Stone Detailing - Requested
10 Rose Petals - Found tending Red Roses
3 Pipe Works - Crafted
Each Statue requires 10 Granite Blocks (Drops from Rocks) and 10 Chisel Kits (Requested)
Each Fountain Pipe requires 5 Iron Bars (drops from Brass and Steel Forges) and 5 Pipe Forms (Requested)
Each Pipe Works requires 5 Fountain Pipes (Crafted) and 6 Pipe Elbows (Requested)