It learns Drill Run by breeding with Beedrill, Forretress, or Pineco. It only gets knock off by transfer, so if that won't work for you, i'd suggest Drill Run/Megahorn/Iron Head/(Poison Jab, Aerial Ace, or X-Scissor) on an assault vest set. It's hard to do w/out Knock Off, so I may consider using leftovers so that you can use Swords Dance instead.
Getting Knock Off and Drill Run on Escavalier in Gen6 is a bit annoying, but you have it in reverse. Megahorn is also an egg move; Escavalier does not get it by level up.
Knock Off: egg move from Gligar evo-line (Gligar learns it at level 10), egg move from Skorupi evo-line (Skorupi learns at level 5) but Skorupi/Drapion is available only through transfer, tutor move in B2/W2.
Drill Run: egg move from Beedrill, Pineco, or Forretress... but they must have learned it from the move tutor in B2/W2. They do not learn it by level-up. Also, Drill Run was not an egg move in gen5.
Megahorn: egg move from Scolipede or Heracross.
So you have to transfer a male Beedrill, Pineco, or Forretress from gen5 which learned Drill Run by move tutor. (Beedrill can also learn Knock Off by move tutor.) Then breed the Drill Run male with a female Escavalier/Karrablast to get Drill Run. If you do not use a Beedrill with Knock Off, then breed a resulting female Karrablast with Drill Run with a male Gligar with Knock Off. Then finally you can breed that female Karrablast (with Knock Off and Drill Run) with a male Scolipede or Heracross for Megahorn.
There is no way to get Drill Run onto Escavalier without transfering from gen5. (As for the final move Iron Head, Escavalier learns that at level 37. The rest of the set is exclusively egg moves in gen6.)
A standard set for Escavalier (Trick Room or not) is
Escavlier @ Assault Vest
Nature: Brave (+Atk, -Spd)
IVs: 0 Spd
252 HP/252 Atk
-Iron Head
-Megahorn
-Knock Off
-Drill Run