When it comes to drilling extruder barrels, by far the hardest part is drilling the very fine die hole at the end. This is often a fraction of a mm and as an effect the tiny drills that you use often snap very easily if used to make a hole that is too deep. Fortunately there is a method to avoid too many breakages.
Step 1. Drill the 3.5mm hole down one end of the barrel, as deep as you dare.
Step 2. drill a hole around 1mm into the other end of the barrel. If it's done enough, then you should break through into the other side of the hole and things are alright.
step 3. If the 1mm deep hole wasn't enough, then use a sander to abraid away the end of the extruder barrel until the small hole you just drilled is almost entirely gone. Then try step 3 again. This can take a while, but saves you the time (and brass) of going too far and either breaking your ultra- fine drill bits, or drilling too deep with your 3.5mm bits.