False Swipe only needs to deal enough damage to knock the target down to 1 HP ; if the hit would otherwise faint it, the move stops at 1 HP instead. If the target is already at 1 HP, False Swipe does no damage.

For a level 45 Ditto

The exact damage number depends on Ditto’s max HP, Defense, IVs/EVs, nature, and the attacker’s stats and level, so there isn’t one fixed damage value. In practice, you want the hit to land for any amount that leaves Ditto at 1 HP , not a specific damage threshold.

Practical rule

  • If Ditto has more than 1 HP left, False Swipe will reduce it to 1 HP if the damage is high enough to KO it.
  • If you are trying to catch it, use False Swipe until it reaches 1 HP, then switch to status moves like sleep or paralysis.

Quick answer

So the answer is: it needs to deal at least enough damage to leave level 45 Ditto at 1 HP, which varies by battle stats and is not a fixed number.

TL;DR

False Swipe doesn’t need a special fixed damage amount for level 45 Ditto; it just has to bring Ditto to 1 HP and can never go below that.