The first special arrow you will get are Poison Arrows. You will learn to make them in the Siberian Wilderness. They are required to beat a certain enemy to progress through the level and are therefore unmissable. The resources you need to make Poison Arrows are Arrows, Cloth and Mushrooms.
Next you will get Fire Arrows. You learn to make them in Geothermal Valley while lighting the signal tower. These are also required to progress through the level and are therefore unmissable. The resources you need to make Fire Arrows are Arrows, Cloth and Oil.
Lastly you will get Grenade Arrows. You learn to make them in The Acropolis while finding a way to clear a barricade. Once again these are required to progress through the level and are therefore unmissable. The resources you need to make Grenade Arrows are Arrows, Cloth and Magnesite Ore.
To select the special arrow type you want press up on the D-pad to select the bow then continue pressing up to cycle between the three arrow types. Now just hold the right bumper to craft the arrows.
Mushrooms and Magnesite Ore are mainly found in caves and tunnels. Mushrooms can also be found in some tree stumps. Oil is found in yellow cans scattered around the map usually in buildings or near machinery. Oil can also be found in caves in small pools that look a bit like campfires. Cloth can be found in crates and Survival Caches and also on the bodies of human enemies. All of these will be highlighted in Survival Instincts.
If you don’t use the bow much I would suggest crafting all 25 of each type as soon as you get them to keep track of what you still need. Craft as many as you can then, once they are full, fire them all and keep crafting. Once you are done just select Reload Checkpoint and you will have all your resources back but will keep the achievement progress. This also works if you run out of resources. Just Reload Checkpoint and keep crafting. Just stay still so you don’t accidentally trigger an autosave.