You have to play as Turkey in Ironman Mode. So, first of all you have to turn the historical focus off and start the game. You have to watch Hungary if they not choose the Balanced Budget in 1936 January 2 then you have to restart it. Its like 40 times for sure its just pure luck. Rush down to "Intervene in the Spanish Civil War" focus and send 8 troops to Hungary when they attack Austria. Win the war and wait Hungary to reclaim Austria-Hungary. You have two options from here:
1. Attack Austria-Hungary with Germany and puppet it. In my opinion its problematic cause the UK maybe guarantee them or you dont have enough war score to puppet them.
2. In my game Germany gave them Fascist support and I boosted the ideology with Spies. You can easily switch to Fascist with Turkey when you have to change Attatürk. Wait for 60% and they will enter the Axis.
In conclusion the hard part in this achievement is to wait for Hungary to choose the Balanced Budget cause its really painful to restart it like 30-40 times. If you have a question then I can help you out, good luck for it.