It helps to be literal here: the most important parameter is the one that is almost never specified: the gradient slope during the region where your main peak elutes.
Mobile phase pH at the point where you inject must match the mobile phase pH at the start of the gradient, or the sample will not be focused at the column head.
Trifluoroacetic acid at 0.1 per cent is the standard ion-pairing agent because it suppresses tailing by neutralising the basic residues, but it also suppresses mass spectrometry signal.
The selectivity of a reverse-phase separation depends on the hydrophobicity of the side-chain profile, which is why two peptides can co-elute even if they differ by a residue.
I would caution against over-interpreting small differences between runs, because the noise floor of the method is larger than most people assume.
The practical summary: specify the method, run the same method on every sample you compare, and use orthogonal techniques to confirm the result.
edited 15 Oct 2024 by gel_pack_warm — fixed an arithmetic slip in the third paragraph