Rise of the Kasai

This trophy is much easier than it sounds. The key word from the trophy description is consecutive, which made me think you must kill 10-in-a-row without dying. The trophy description actually doesn't say anything about you dying, it simply says to kill 10 consecutive enemies while Player's health is below 25%. In other words, you can die and your cumulative count does not reset unless you exit the level or kill your next enemy when your health is over 25%.

Here's what I mean:

1. Start up whatever level and sub-area that you want.
2. Run up to a bunch of enemies and let them beat on you. Do not attack them at all.
3. Wait until your health bar turns red.
4. Once your health bar is red, start attacking enemies to kill as many as you can.
5. If you happen to die, the game will start you at the beginning of this sub-area. Repeat steps #1-4 again. Keep doing this until you get your 10th kill while your character's health is less than 25%.

It may help to go into the Options menu and change the game configuration such that your character's health bar is always displayed. It also may help to use the Wimpy Enemies cheat (though it's definitely not necessary). The trophy will unlock immediately once you have satisfied its conditions.