You do not need to use a specific race to get this achievement however it is probably easiest with the Dwarf since that race has the most essence. You can buy rez first round with any race.
If you have a microphone talk to your team mates, let them know that you have purchased rez and you can bring them back. Beginning of the round you may want to just activate rez (it will not do anything but it is a visually confirmation that you have the ability). A good strategy to use is to follow a majority of your team mates; if someone dies then rez them. Again communication is key here. Run around and keep an eye out for an orange body on your HUD, it will be the location of an ally who is dead and can be rezed.
This is not going to be an achievement you can grind out in a match; it will take a while.
Benefits of rezing people is that you get more money for each rez, then you buy weapons and you can then work on weapon achievements or buy other powers. Tree of life is a good power for the team medic as you will earn money as well.