For this example I'll be using the Hallway Fizzgrid below.

The hallway:

[*][*][*][*][*] [*][*][*][*][*]
[_] [_] [T] [_] [_] [2][3][_][_][_]
[_][_][_][_][H] [1][4][_][_][_]
[*][*][*][*][*] [*][*][*][*][*]

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Here T represents a trooper and H represents Han Solo.

Spaces 1, 2,3 and 4 are spaces taken up by a Nexu.

Han grants bonuses to an adjacent defending space of +1 surge cancel.

In this case if the trooper chose to attack space 2 the Nexu would be granted this bonus.

The attacker could choose to target space 4, they still have line of sight as the Nexu does not block line of sight to itself and the trooper can trace LOS.

When rolling and checking for accuracy does the trooper need to have 3 or 4 points of accuracy?

I'm assuming it's 4 as the attacker must declare a target space, but the RRG under attacking defines targets as a hostile figure, not space.

The way I read the rules the attacker could target the Nexu, and choose the rear space as the targetted space for drawing LOS etc, but the check accuracy step only requires accuracy to count spaces to reach the target. It seems like an easy way to game the system to require one less accuracy and avoid Han's ability.

You're assumption is correct. You will need 4 accuracy.

Since the first step of an attack is "Declare Target" (pg 5, RRG) reads:

"...the figure performing the attack (referred to as the attacker) declares one eligible target for the attack (referred to as the target)."

And rules under "Target" (pg 24 RRG) state:

" If the target is a large figure, the attacker must target one space that the target occupies. This space is used for determining line of sight and some abilities."

So with large figures, whenever the term "Target" is used, you must use the declared target space.

Thanks!