Wizkids Rules!

Nocturne: T.J.
While Nocturne is active, once per turn, when your opponent uses a Global Ability with 1 target, you may redirect the effect to another legal target.

How does Nocturne work when an action has multiple targets? Would she be able to redirect all of the targets or only a single target? If only one target, what happens if the targets are chosen sequentially? Here are some actions to consider.

Raised Shields: Basic Action Card
Two target character dice you control get +1A and +1D.
*/** Also, they gain Overcrush.

Both targets chosen at the same time, with the same effect.

Cone of Cold: Basic Action Card
Deal 1 damage to target character die, deal 2 damage to a different target character die, and deal 3 damage to another different target character die. You may only use this action if there are at least 3 character dice in the Field Zone.

Three targets are chosen (presumably at the same time) and with different effects.

Rolling Thunder: Basic Action Card
Deal 1 damage to target character die. If it isn't KO'd, deal 2 damage to another different target character die. Repeat this process, increasing the damage by 1 each time until either a character die is KO'd or there are no remaining targets.

Do you select one target for Rolling Thunder at a time or all at once? in either case, when does Nocturne choose which target to redirect? Can Nocturne be used to redirect one of the earlier instances of damage to KO a die, thus stopping the sequence?

From your questions we assume you are referring to the Nocturne – Shadowy Lineage card:

While Nocturne is active, the first time your opponent uses an Action die each turn, you may redirect the effect to another legal target.

How does Nocturne work when an action has multiple targets? Would she be able to redirect all of the targets or only a single target? If only one target, what happens if the targets are chosen sequentially?

In such a situation, the effect for each target can be redirected to another legal target.
Addressing the Action die abilities you cited:
Raised Shields: the +1A/1D bonus would be redirected to two other legal targets.
Cone of Cold: each instance of damage (for the 3 different targets) would be redirected to a different legal target.

Do you select one target for Rolling Thunder at a time or all at once? in either case, when does Nocturne choose which target to redirect? Can Nocturne be used to redirect one of the earlier instances of damage to KO a die, thus stopping the sequence?

Since each instance of damage has a condition, you would check if the condition is met before continuing to apply damage.
Example: Deal 1 damage to a target character die. Nocturne would redirect that damage to another legal target. If that target, to which the 1 damage was redirected, is not KO’d Rolling Thunder’s ability would continue and deal 2 damage to a different target die. Nocturne would redirect that 2 damage to a different legal target. Continue with the ability until a die, to which the damage was redirected, is KO’d or there are no remaining targets.

Likewise for Action die abilities with multiple effects in which a subsequent effect (as stated sequentially in the ability) has a condition, the application of the subsequent effect is based on the resolution of the previous effect. For example:

Arctic Breath: Deal 1 damage to target character die. Put a STUN token on a different target character die's card.

This ability has two separate effects with the second effect having a condition. In this situation (interacting with Nocturne), you would resolve the first effect (damage application then redirect) then complete the second effect based on the result of the first effect.
Example: 1 damage is dealt to target Character die [A]. Nocturne redirects that damage to target Character die [B]. A STUN token is placed on target Character die [C]. Nocturne can redirect the placement of that STUN token to any different Character die, except Character die [B], including Character die [A].