Best place to try this is the first boss. Best weapon to use 609mm Handcannon. Timing is very very important. It might take a couple of practice runs.
Get your health down to halfway before you even shoot at the boss, by either selfinflicted damage or enemy fire. Now take off around 3 quarters of the bosses health. Again get your health down now to around 10-20%. You should now be able to gauge how long it takes to reduce both your health now and the bosses, timing is everything. When you're about to kill the boss ensure you have enough time to kill yourself. When you do kill the boss, quickly kill yourself by constantly firing the hand cannon at the ground and if you manage to die during the explosion phase of tthe achievement will pop.
Tips - Use the 609mm Handcannon, wait until the Caketown Run as this removes enemies meaning the timing is easier to gauge.