By making sure a lot of people have a small stake in it, and making sure that everyone involved is afraid to be fired if things are not properly handled.

The judicial system in my country, Portugal, is a moderate example of success (when it comes to not being too partisan, effectiveness and speed is not good, mostly due to legislative and governing incompetence, and incompetence from public prosecutors), but the basic way it works afaik is that the superior council of magistrates, which is tasked with supervising judges has a 40% stake internally elected (by other judges), a 40% stake by parliament and a 20% stake by the President.

Because the government is parliament bound and is NOT the President, then the executive power is separate from the president.

Finally, here the president has a more “cerimonial role” with his real power being fundamentally to be a last resort when all turns to chaos. So far it has worked well-ish