How does the Constitution guarantee judicial independence? Do you think judges have enough independence? Too much?

Yes, constitution guarantee judicial independence.

Usually, the independece is enough.

The system could be better suited to reach better levels of justice, but would be exagerated to say that justice has 'too much' independence.

Explanation:

The US constitution was inspired by the work of Jhon Locke, who was one of the first authors who proposed division of powers in the XVII century. The central idea is to avoid the concentration of power in one person or a single institution. In this case, the judges has plenty authority to investigate and judge anyone who commit a crime. Nor political or policial autorities has influence on judges, and this is guarantee by the constitution.

In some cases this principle is susceptible and that's why is necessary the intervention of supreme court, in some cases, when political forces, for example, try to violate these rules stablished by the constitution.