I generally interpret the player’s ready statements as charitably as possible, without too much stress on the mechanics of triggering. In this particular case, the player probably isn't aware of the Dodge action, which gives disadvantage to all attacks that you see coming (and also advantage on Dex saves). So, in this specific situation, I probably would tell the player that they could just do that for the round.
Or, if they specifically want to focus on one expected incoming attack and not just be generally on guard, I might instead allow their reaction to increase cover by one level against just that attack. That's not supported directly by any rule section, but it seems like a reasonable way to give mechanics to what they're trying to do.
In general, I try to avoid getting into situations where the exact timing of readied actions vs. other readied actions is even an issue. The whole "everyone takes turns but it's really happening all at once except kind of not really" experience of D&D combat takes some suspension of disbelief, and arguing too finely about the resolution of readied actions skirts close to the edge of breaking it.
If this is about being prepared before a combat actually starts, and people start throwing around plans to ready actions when I also want the adversaries to be prepared, I'd rather say "Okay, everyone on both sides is itching to go. Let's roll initiative to see how it goes down." If both sides indicate that they're ready for action in some way, this plays out as lack of a surprise round, rather than a round with a bunch of confusing adjudication of the timing of readied actions.
Other times, players want to ready actions during combat. From experience, most of these times they are doing so because they want to interrupt something — but by the rules, most reactions happen after their trigger is complete. That leads to the rules not supporting perfectly reasonable behavior, which leads to breakdown of suspension of disbelief, which leads to lack of fun.
One could be strict about the wording of exactly what was given as the trigger: "Ohhhh, you said you wanted to shoot him if he attacks, so he shot the little orphan before you did anything!" But, I think it's better to say "You want to shoot if the ruffian looks like he's starting to attack, right?" and go from there. If the enemy is also readying an action to make that attack when something else happens, I error on the side of letting the player attempt what they say they want to try.