Alexanders stage is surrounded and separated by spikes, that actually are helpful. You can use the low damage spikes to get invincibility for a short time. The spikes also have higher priority than the boss hitbox itself, this means if Alexander and the spike hitbox touch you you'll receive damage from the spikes, not from Alexander. Don't get surrounded by the flying skulls, defeat them as fast as possible and only hit Alexander when it's secure. If you let the skulls live for too long you won't be able to evade anymore.
If you beat this boss consider yourself good at games.