Performed all 8 of the Vigor combinations.

First of all you will need to collect all Vigors. Some of them are missable.
For all their locations please see Well Rounded.

You can do the combos at any time, against any type of enemy. If you restart checkpoints your progress will stay. Keep restarting checkpoints if you are out of salts.

List of all Vigor Combinations:

1) Possession + Devil's Kiss
2) Possession + Shock Jockey
3) Murder of Crows + Devil's Kiss
4) Murder of Crows + Shock Jockey
5) Bucking Bronco + Devil's Kiss
6) Bucking Bronco + Charge
7) Undertow + Shock Jockey
8) Devil's Kiss + Charge