To transmute an Apparatus you will have to find the Recipe: Apparatus
Once you have found this Recipe you will see what ingredients you need. In this case, to transmute an Apparatus, you will have to need the following ingredients: Legendary Blink ; Legendary Lightning Gun and a Gadget.
Now here comes the "hard" part.
You see you need Gadget. You will have to obtain this Recipe: Gadget
Gadget needs the following ingredients: Rare Dark mist , Legendary The Lightning(Destiny Card) and a Gizmo.
Here you see you need Gizmo. So you will have to find and obtain the Recipe: Gizmo
Gizmo needs the following ingredients: Uncommon Flash Bomb , Rare Lightning Gun and a rare Wildcard.
If you want to go for this, make sure you have the right gear! So make sure you have one weapon with : Find ..% more items
("Finger of Chaos" has: While equipped: Find 40% more items)
And your other weapon should have: While equipped: Find better items
It doesn't matter if you equip it first or equip second, as long as you have these two weapons on you, you will get and find the recipes!
So get a weapon with: Find better items and a weapon with find ..% more items. You will see not all Legendary weapons have those stats. Some of the uncommon and rare weapons have those stats.