@safreek shim bleeds are a piece of piss. As per that pic in the linked article, just take the while top cap off (after making the reservoir level!) so 2 bolts on the old models. You can just fill up the reservoir, pump the lever, repeat until brake feels firm and then seal it up. You don't need to do the whole process of you just want a quick solution.
Otherwise you just need a piece of hose that fits (aquarium hose from pet store or bunnings etc) and run that into a vessel of some sort (eg emptt water bottle). Spanner for the bleed nut on the calliper and away you go. This is the unpopular gravity bleed. Alternatively head into the pharmacy for a big syringe (without needle). Fill that with oil, attach hose, connect to nipples, crack nipples and squeeze that shit on nice and steady. Don't forget to open the reservoir first. Oh and also drain the system before you start pumping! Otherwise you'll probably get shit everywhere. So open resevoir, drain system, dial up your syringe, pump it in, close off the nipples, top up the reservoir, seal it up, enjoy reliable braking