Anecdotal, of course, but worked for me on my Warsaw - Sydney trip, where I brought two bikes (one road, one mountain).
I got 2 cardboard bike boxes from my local bike store (they throw them away - at least in my case - so you can get them free). They're fairly sturdy, definitely more solid then your typical cardboard box. In order to fit the bikes into boxes, I needed to take the wheels, saddles, forks and handlebars off. Didn't need to unscrew brakes - just needed to realign the handlebars to a more vertical position.
I bought foam pipe insulation, cut it into pieces of fitting size and wrapped it around the frame elements (didn't wanna crack it - carbon, I think aluminum/steel might require less care), attaching it with cable ties. I also bought a whole lot of bubble wrap and triple-wrapped everything. Since I had limited luggage allowance, I didn't take a suitcase, instead i stuffed my clothes in with the bikes for even more protection ;)
Taped the boxes shut and wrapped them with plastic wrap.
The bikes weren't damaged, although the same cannot be said about boxes. One axle popped through one of the boxes (undamaged) and the plastic wrap was torn badly.
Naturally, your mileage may vary. Luggage handlers aren't particularly gentle.
Edit: One thing you may want to check first is the luggage size limit (not just weight). I flew Emirates, their rule is that the sum of dimensions of each piece of luggage cannot exceed 300 cm. As far as I remember, the boxes were something like 147x80x30, so they fit in with a bit of room to spare.
One answer suggests having it delivered. This greatly depends on your starting point and destination - I checked the pricing for a delivery from Poland to Sydney - would literally cost me more than flying back from Sydney, picking it up and flying to Sydney again. Can be very prohibitive.