Buy one Sea Tea. It increases your soul's movement speed for one battle. Useless for the Green part, but for the spears it's extremely nice, especially later on.
Take one of the Inviciblity Frames increase items.

Undyne The Undying
List of Moves

1. ↑ ↑ ↑ → ↓ ← ↑ ← ↓ → ↓ ← ↑

2. ← → ← ← → → ← → → ← → ← → ←

3. ↓ ↓ ← ← ↓ → ↑ ← ← ← ← ↑ ← ↓ ↓ ↑ ↓ ←

4. dodge floating arrows (hint: little movement)

5. dodge upward arrows (pattern of arrows is) left, middle, right, left, middle, right, left, middle, right, middle, right, left, right, middlez

6. ← ↑ → ↓ ← → ← ↑ ↓

7. ↑ ↑ ↑ ↑ ← ↑ ↑ ↑ ↑ → ↑ ↑ ↑ ← ↑ ↑ ↑ → ↑ ↑ ↑

8. ← ↑ ← ↑ ← ↑ ← ↑ * → ↓ → ↓ → ↓

9. dodge circle of arrows (hint: slide through between 2 arrows)

10. dodge circle of arrows (hint: slide through between 2 arrows)

11. ← ↓ → ↑ * ↑ ← ↓ → * ↑ → ← ↓

12. ← → * ↑ * ← → ↓ * ↓ * ← → ↑ * ↑ * ← → ↓ * ↓

13. ← * → * ↓ * ↑ * → * ← * ↑ * ↓ * ← * → * ↓ * ↑ * → * ←

14. → ← ↓ ↑ ← ← ↑ → ← ↓ ↑ ← → ↓ ↓ ↓ ↓ → ↑ → ↑ ← ↓ ↑

15. Dodge circle of arrows 2 types

16. Dodge circle of arrows 1 type

17. Dodge floating arrows

18. Dodge upward arrows (pattern of arrows is) middle, right, left, middle, left, middle, right, left, right, middle, right, left, middle, left, middle, right

19. Dodge circle of arrows 2 types

20. Dodge circle of arrows 1 type

Undyne dead

* means arrows change from either normal to gold or gold to normal

Thanks to Derpuccino on Reddit

Dodge in a circular motion motion. When a set of spears appear, wait until they slow down a little so you can spot an exit. For the more rapid version of the attack, just watch for the immobile spawning spears and just keep moving. The spears which reach their converging point fade out and do no damage. If you're having trouble here, I suggest you don't use the pie or you're definitely going to have trouble later. If you have Dog Residue, you can get some Dog Salad and leave it to luck.