This use of the expression feels kind of weird, and it wasn't easy to figure out what was bugging me, but I think I got it (kind of).
First, "Tout individu normalement constitué" is mostly used for medical or physical uses. It can be used by extension for other things, humorously, but it's not its main purpose.
Also, conditional isn't the best tense to use with it. The expression is (I think) mostly meant for something called a "vérité générale" (general truth), like "water boils at 100°C" or "human normally have two arms and two legs". (You should look up "présent de vérité général", it's not a tense, it's a value of a tense).
So I'd use the expression like this : "Tout individu normalement constitué peut survivre au maximum 3 jours sans eau". If you have to use conditionnal it would be like: "Un être humain normalement constitué devrait pouvoir escalader cette facade sans problème".
It's more to talk about physical (or intellectual) capabilities than a general term for "anyone".
I'd say "N'importe qui aurait du mal avec ..."
By the way, "à juste titre" means "with reason", as in "one would be right to do so". It's generally when you make assumptions that happen to be true.
Ex: "L'ours est considéré à juste titre comme un des animaux les plus dangereux qu'on peut rencontrer en France"
You can "assume" or "fear" something with reason, but not "have difficulties with something with reason".
The line is pretty thin, you can "find something hard" with reason but not really "have troubles with something with reason". (I hope I'm being clear)