Direct link to an animation of catching a rocket with a helicopter: https://youtu.be/joONWIGtcdY?t=858
But it's been done[1].
[1]: https://en.wikipedia.org/wiki/Fulton_surface-to-air_recovery...
Having the booster survive the re-entry heating and aerodynamic loads while only using passive methods to slow it is the hard bit.
Looks like the video got truncated after the livestream.
"[The helicopter] would be gigantic. The rotor diameter would be over 120 meters (400 feet). Its empty weight would be over 200,000 kilograms (450,000 pounds), with a useful load of nearly 250,000 kilograms (550,000 pounds), for a gross weight of a whopping 453,000 kilograms (1,000,000 pounds)"