Yes you can get it by leveling up
If you have an Abra, the best hypnosis Pokemon is alakazam. So catch an Abra, evole it to a kadabra, the evolve it to an alakazam to have the best hypnosis Pokemon
Most psychic types can learn hypnosis most normal types can learn rest. Here are some examples: Snorlax, Hypno, Alakazam, Noctowl.
Alakazam does not evolve
Alakazam
Different types of hypnosis are stage hypnosis, covert hypnosis (for persuasion), self hypnosis, and hypnosis for specific issues such as weight loss or smoking cessation.
First You need an Abra Evolved into Kadabra. Then You need to Trade Kadabra to a person where it will evolve to Alakazam. Then that person MUST trade Alakazam back for you to have Alakazam in Pokedex.
Trade Kadabra to get Alakazam, and Haunter to get Gengar.
Kadabra evolved into Alakazam when it was traded.
kadabra evolves into alakazam when he is traded.
Alakazam doesn't evolve.
Abra only evolves twice: into Kadabra and Alakazam. Alakazam does not evolve, as it is the final form of Abra.
The duration of Alakazam the Great is 1.47 hours.