Does not "So Fast" negate all of Icathian Rain?

Yes, Not So Fast negates the entire Icathian Rain spell.

According to a RiftJudge FAQ regarding this specific interaction:

Q: When my opponent plays Icathian Rain and I play Not So Fast on one of the targeted units, is the whole spell cancelled or just the damage to that one unit? A: Ruling: The entire Icathian Rain spell is countered. Not So Fast counters the spell itself, not just individual instructions. If Icathian Rain targets at least one of your units, you can play Not So Fast to counter it, preventing all six instances of 2 damage regardless of what they were targeting.

Why this happens:

1. Countering: Per Rule 425.1.a, a card that is countered does nothing and is cleared from the chain.
2. Scope: Not So Fast targets the spell itself, not the individual damage instances. Because Icathian Rain is a single spell on the chain, countering it removes the entire object from the chain, preventing all of its instructions from executing.
3. Condition: As long as Icathian Rain chooses at least one friendly unit or gear as a target, the condition for playing Not So Fast is met.