You can acquire an Alakazam via the Ditto Glitch but in terms of evolving a Kadabra into one, unfortunately you need another Gameboy with a Red/Blue/Yellow cartridge.
To acquire Alakazam in Yellow via Ditto Glitch, be sure to have Fly, Dig and/or Teleport at your disposal and do the following steps.
1) Find a "Glitch" Trainer. A Glitch Trainer is someone who activates from 4 steps away, meaning as soon as he comes into viewing range, they activate. The key is to press start to open the menu prior to the Trainer yielding "!" and initiating a Trainer battle. You will want to Fly or Teleport away. Fly is best because you can choose where to go and afterwards the menu will be unavailable so its best to go to a place where you can battle another trainer.
2) Find a Trainer you haven't battled yet and then battle them by having them see you and having to walk at least 1 space to fight you. Defeat the trainer however you see fit.
3) Fly to Cinnabar Island and go into the Basement. From there you will want to run into a Ditto. Withdraw or defeat all other Wild Pokemon until you do. When you do run into a Ditto, switch in a Pokemon who has a Special Stat of 149. Ditto will then transform and take on the stats of the Pokemon in question(notably the special stat of 149). Run from the battle after it transforms.
4) Dig/Teleport out of the Mansion and proceed back to the area where you met the Trainer in Step 1. Upon doing so the menu will open automatically(this is good). Press B to initiate the battle against a level 7 Alakazam. Forget what moves it knows but it does know Teleport so be sure to have a Pokemon ready that can put it to sleep to prevent it from getting away.
The downside to a Ditto Glitch Alakazam is that it wont have the moveset that one would have if evolved from Kadabra. However, this is the only way people with just 1 game can complete the Pokedex without the use of a second Gameboy.