All basic tools: yes.
All upgrades to the tools: no.
All Bosses: No. But with backup + reload yes.
Now I count the Great Colored Carp and the Great Serpents as bosses, though they don't give a boss memory.
I don't count the Headless and the minibosses. Just do the minibosses as soon as they're available, if you want to fight them all. Some become unavailable later after the key events:
So minimal time investment strategy to experience all bosses:
You have now fought all the bosses.
You can now even get all remaining endings if you backup + reload the save after defeating Isshin, the Sword Saint, before speaking to Kuro at the Silvergrass Field for the last time.