Spider Climb. The spider can climb difficult surfaces, including upside down on ceilings, without needing to make an ability check.

Web Sense. While in contact with a web, the spider knows the exact location of any other creature in contact with the same web.

Web Walker. The spider ignores movement restrictions caused by webbing.

Adaptive. When it takes damage for the first time after a long rest it instead take no damage, its maximum HP is increased by twice the maximum damage that the attack could have dealt and it gains immunity to that type of damage. When it is hit for the second time it takes no damage and its max HP is increased by twice the maximum damage that the attack could have dealt and it gains resistance to that type of damage. Additionally it gains two attacks that deal the same types of damage as the first two attacks that hit it. This resets on a long rest. 

Bite. Melee Weapon Attack: +5 to hit, reach 5 ft., one creature. Hit: 7 (1d8 + 3) piercing damage, and the target must make a DC 12 Constitution saving throw, taking 9 (2d8) poison damage on a failed save, or half as much damage on a successful one. If the poison damage reduces the target to 0 hit points, the target is stable but poisoned for 1 hour, even after regaining hit points, and is paralyzed while poisoned in this way.

Web (Recharge 5–6). Ranged Weapon Attack: +5 to hit, range 30/60 ft., one creature. Hit: The target is restrained by webbing. As an action, the restrained target can make a DC 12 Strength check, bursting the webbing on a success. The webbing can also be attacked and destroyed (AC 10; hp 5; vulnerability to fire damage; immunity to bludgeoning, poison, and psychic damage).

Magicwave. Spell, DC 12. A wave of magic sweeps out from monster. Each creature in a 15-foot cube originating from spider must make a Constitution saving throw. On a failed save, a creature takes 13 (3d8) [damage type as the first attack that hit it] damage. On a successful save, the creature takes half as much damage.

Touch. Melee Weapon Attack: +5 to hit, one target. Hit: 10 (2d6 + 3) [damage type like the second attack that hit it] damage. Leaves magic goo on target. Until a creature takes an action to get rid of the goo, the target takes 5 (1d10) [damage type like the second attack that hit it] damage at the start of each of its turns.