Blutsaugher
Once you have earned 10 of all the achievements for the Medic, you'll unlock the Blutsaugher. This is a new syringe gun which does not score critical hits, but it transfers a bit of the health from each hit against an enemy to the medic. It is not an exceptional weapon, which makes sense, at it would be bad to give the Medic too much offensive power. It does give the Medic a little bit of extra health, however, making it much easier to beat a fighting retreat. There is little reason not to use this once you earn it.
Kritzcrieg
Once you have 16 achievements, you'll earn the Kritzcrieg. This is replaces the normal medigun with one that, rather than providing invulnerability as the ubercharge special, provides a 100% chance to perform a critical hit. This can obvious be devastating to a front line, although it is probably not as useful against defense positions that are defended by well-placed sentries. They are too deadly, and will kill whoever is ubered well before they can do much damage, unless you uber a Demo-man who is extremely good at what he does.
Ubersaw
Earned when 20 achievements are unlocked, the Ubersaw is a replacement melee weapon which, unlike the regular saw, charges your ubercharge! This is less useful than you might think, because come on, how often is a Medic in melee range? Usually, it is only a moment before the Medic is stabbed in the face by a spy. That said, if you do manage to use it, then it is extremely handy. And besides, there's no real reason to carry the normal saw after you have this.