A Y-Wing with a TLT declares an attack. Latts spends a target lock she has on the defender to reduce his agility by 1.

Does his agility stay -1 for both of the TLT shots? Do they both count as the same attack? Or only the first one.

TLT says "Perform this attack twice". It's two attacks, although the second one doesn't include the Declare Target step, which is why R3-A2 can't trigger twice off a TLT alone. Latts only helps against one of the TLT shots.

TLT's are two attacks, the second of which skips the declare a target step. Since Latts ability impacts 1 attack, only the first attack would be against the reduced AGI.

roger roger

and spelled out with a specific FAQ

Latts Razzi’s ability is used when a ship is declared as the target of an attack. Therefore, when used with an ability that performs multiple attacks against the same target such as Cluster Missiles or Twin Laser Turret, Latts Razzi’s ability can only be used during the first attack and only applies to the first attack.

You can also compare this to Miranda who only gains one shield/dice and only one of her tlt attacks is effected this way.