This is pretty self explanatory. You only have to survive through 8 waves, and even if you do not make it to wave 10 and extract the achievement will still pop.
Some tips may include only equipping a melee weapon to keep yourself from succumbing to the urge to shoot those pesky fleeing enemies attempting to draw you away from the cryopod. Making sure you are using level 30 weapons and warframe should be a no brainer, even though I didn't follow either of these tips myself. freddyflask
advises that his achievement did not pop until he went with no ranged weapons equipped at all. So if you are having issues with getting it to pop make sure you are only equipping a melee weapon.
I completed this achievement solo on the mission for Lith on Earth. This is a low level mission. Even though my melee weapon is level 30, my suit was only level 24 at the time as I had recently polarized a slot. On this mission the enemies have a lot of hiding places and they tend to use them and their hiding tends to keep them from attacking the cryopod full on. I took my time, hugged the cryopod and let the enemies come to me. Since they love to run away and draw you away from the cryopod it is easy to chase them down increasing your chances of failing the mission due to them destroying the target. I recommend staying inside the ring until you are down to the last few enemies on each wave. There aren't any difficult enemies until around wave 8 when you will get a few shielded guys which still aren't very powerful.
My achievement popped half way into wave 9 so I believe you could just let them kill you after wave 8 and still get the achievement without a problem if you didn't feel like going to wave 10 and extracting.