Your achievements and stats can be viewed in Steam under: "Community -> My profile -> View all my games -> Team Fortress 2 (view stats)" These achievements can only be earned while playing the medic class, by getting a certain number of these achievements you unlock new medic weapons:
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Autoclave → Assist in burning 5 enemies with a single ÜberCharge on a Pyro.

Autopsy Report → Provide an enemy with a freezecam shot of you taunting above their ragdoll.

Bedside Manner → Be healing a teammate as he achieves an achievement of his own.

Big Pharma → Assist a Heavy in killing 20 enemies, where neither of you die.

Blast Assist → Assist in exploding 5 enemies with a single ÜberCharge on a Soldier.

Blunt Trauma → Assist in punching 2 enemies with a single ÜberCharge on a Heavy.

Chief of Staff → Accumulate 1 million total heal points.

Consultation → Assist a fellow Medic in killing 5 enemies in a single life.

Doctor Assisted Homicide → Assist in killing 20 nemeses.

Does It Hurt When I Do This? → Kill 50 Scouts with your syringe gun.

Double Blind Trial → Deploy an ÜberCharge within 8 seconds of a nearby enemy Medic deploying his.

Family Practice → ÜberCharge ten of your Steam Community Friends.

First Do No Harm → Play a full round without killing any enemies, and score the highest on a team of 6 or more players.

FYI I am A Medic → Use your bonesaw to kill 5 Spies who have been calling for 'Medic!'.

Grand Rounds → Heal 200 teammates after they've called for 'Medic!'.

Group Health → Work with 2 other Medics to deploy 3 simultaneous ÜberCharges.

House Call → Join a game that one of your friends is in and then deploy an ÜberCharge on him.

Hypocritical Oath → Kill an enemy Spy that you have been healing.

Infernal Medicine → Extinguish 100 burning teammates.

Intern → Accumulate 7000 heal points in a single life.

Medic Milestone 1 → Achieve 10 of the achievements in the Medic pack.

Medic Milestone 2 → Achieve 16 of the achievements in the Medic pack.

Medic Milestone 3 → Achieve 22 of the achievements in the Medic pack.

Medical Breakthrough → Assist in destroying 5 enemy Engineer buildings with a single ÜberCharge on a Demoman.

Medical Intervention → Save a falling teammate from dying on impact.

Midwife Crisis → Heal an Engineer as he repairs his Sentrygun while it's under enemy fire.

Peer Review → Kill 50 Medics with your bone saw.

Placebo Effect → Kill 5 enemies in a single life, while having your ÜberCharge ready, but undeployed.

Play Doctor → In a team with no Medics, be the first person to switch to Medic after a teammate calls for 'Medic!', and then heal 500 health.

Preventive Medicine → Block the enemy from capturing a control point with an ÜberCharged teammate.

Quadruple Bypass → Heal a teammate who's taking fire from 4 enemies at once.

Sawbones → Hit enemies with your bonesaw 5 times in a row without dying or missing.

Second Opinion → ÜberCharge 2 teammates at once.

Specialist → Accumulate 10000 heal points health in a single life.

Surgical Prep → Have an ÜberCharge ready before the Setup phase ends.

Trauma Queen → Deploy 3 ÜberCharges in less than 5 minutes, and assist in 5 kills during that time.

Triage → Deploy an ÜberCharge on a teammate less than a second before they're hit by a critical explosive.

Ubi concordia, ibi victoria → Assist in killing 5 enemies on an enemy control point, in a single life.

You'll Feel a Little Prick → Assist in killing 3 enemies with a single ÜberCharge on a Scout.