This achievement requires ten cumulative deaths before reaching level 15.
Start a new game on Easy, unequip your armour and throw your grenades on an adjacent tile. This will work with any characters except the Scout, Seeker and Striker who have no grenades and the Lich who has to deplete both health and psi points before death. The same method would likely work on Normal but I've confirmed that all other characters have enough grenades to kill themselves on easy.