It all depends on what one considers an achievement, but that's clear, we all know that already.
If I want to take "achievement" as meaning "completely game-changing moment which provided huge innovation to bioinformatics and also bench-biology", then one of the major moments for me was the realisation by Karlin and Altschul that the distribution of optimal alignment scores between a query sequence and a set of unrelated database sequences is better described by the extreme value distribution, rather than a normal distribution (Karlin and Altschul, 1990, Proc Natl Acad Sci U S A, 87, 2264-8).
This has enabled us to make much more accurate estimations of how likely it is that two sequences share a common structure/function; this allows us to obtain a "new" sequence and already, after a simple analysis (e.g. carrying out a BLAST search) find another sequence that is likely to have a similar function; we might, for example, already know that it is extremely likely to be a kinase; without that insight, it might take a very long time, using "just" bench methods, to arrive at the same conclusion.
Thus, this achievement has saved huge amounts of time and money in the field of biomedical research; i.e. without this achievement we would presumably be much (much much...!) less advanced in this knowledge domain than we have become.