I'm asking specifically about the lovely Magus of the Balance if that'll help. So for example, If I were to attack with a theoretical 20/20 Savageborn Hydra, and then my opponent declares block with Magus, would my opponent still be able to sacrifice the Magus after declaring block?
Yes, that's possible. Declaring blockers is one of the steps of combat, and after declaring blockers the Hydra becomes blocked:
509.1h An attacking creature with one or more creatures declared as blockers for it becomes a blocked creature; one with no creatures declared as blockers for it becomes an unblocked creature. [...] A creature remains blocked even if all the creatures blocking it are removed from combat.
After that, there is time for the players to play spells or abilities:
509.4. Fourth, the active player gets priority. (See rule 116, "Timing and Priority.")
Combat damage is only dealt in the next step:
- Combat Damage Step
510.1. First, the active player announces how each attacking creature assigns its combat damage, then the defending player announces how each blocking creature assigns its combat damage. ...
so it's possible to sacrifice the Magus before it's killed by the Hydra, and the Hydra won't deal combat damage to your opponent (unless it somehow gained Trample) since it's still blocked.