Standard slash on X (but i almost never use it to fight, mostly to extend air time if needed); Hammer powered up on Y (usually my main attack); and for bosses, Light Spear powered up on B (bomb probably works well, too).
With the spider, i did it on the second try (and only died at the part where you have to run away) i just kept myself in the air using the hanging lamps w/LB, and just kept blasting him on the head with the spear over and over.
I switched the spear to the light-area-power, just when it requires you to, and came down to the ground only to replenish the mana.
The toad similar deal, but even easier, as you can just swim left and right, jump out of the water and blast it with the light spear, and go back in, rinse & repeat.
Compared to what i saw my brother go through in Hollow Knight, this seemed like a walk in the park, tbh.