My personal tip for By My Hand Alone
So after trying so hard to get all the kills in the earlier rounds only to get screwed out of a kill sometime during rounds 10-12 (3 times on round 12 alone) I decided to farm oil tanks in round 9 to make rounds 10-12 easier. I posted this solution on another site but I'm posting in here in order to help as many people as possible.
If you're struggling in rounds 10-12 like I was, I worked out a way to make those last 3 rounds VASTLY easier.
Using this method I only needed 2 grenades the entire game (one for the music box guy in round 8 and round 12), and still had 3 mana vials and 3 health vials left at the end of round 12 when I got my achievement.
Be warned: This method takes TIME. Don't do the oil cans until the end of round 9 just in case you get screwed on an earlier round. If you wind up failing anyway after doing this (I failed twice after setting up my oil cans), you will waste about 20 minutes each attempt setting this up. BUT, if you do it right you should get it within a few tries, as opposed to who knows how many hours of failed attempts the normal way.
Step 1: Complete rounds 1-5 as normal, taking out enemies with whatever means you're comfortable with. Personally for me, beginning round 3 I grab the oil tank and stand on the far stairs from the spawn and throw it at the first 2 enemies I see fighting, or the nearest enemy to my left. Leave the last enemy alive each round until another oil tank spawns to use at the start of the next round.
Step 2: Complete round 6 (and 7 if you can, but it's not necessary) WITHOUT using bend time. I was able to complete rounds 6-8 without using bend time by using the same oil can method as above to clear out the first enemy, shooting the 2nd and 3rd, and leaving the 4th alive to respawn an oil can for the next round.
Step 3: On round 9, LEAVE THE LAST ENEMY ALIVE. Preferably, leave an assassin alive as the soldiers have a tendency to get eaten by rats occassionally while you're setting up the cans (step 4) and it's really frustrating.
Step 4: While hiding from the last enemy, let an oil can spawn and place it on the Tall Boy spawn nearest the oil can dispenser. Hide and wait 1 minute for another to spawn and repeat. Place 5 oil cans at the nearest tall boy spawn, then proceed to place 5 at the far tall boy spawn. Position them close together without being so close as to risk killing/damaging yourself. You can lure the last enemy away from the oil can/tall boy spawns then blink away from him to disappear if need be. Just let your mana refill if you do.
Step 6: After placing 5 oil cans at each tall boy spawn, kill the last enemy. Kill the merchant ASAP, then pull out your bend time and face the tall boy spawn near the oil can dispenser, as round 10's tall boy has a tendency to spawn there.
Step 7: Whether you see a tall boy or not, hit your Bend Time after the round starts. Shoot the oil can if the tall boy is there, or turn to the other spawn and shoot those oil cans. This will one shot kill the tall boy and you'll still have Bend Time left to clear THREE enemies.
Step 8: Once again, leave the last enemy alive and replace the 5 oil cans you destroyed. Kill the last enemy, and get in position for round 11 in the same method. Round 11's tall boy usually spawns opposite from where 10's did, at least it always did for me.
Step 9: Complete round 11 the same way (bend time, shoot oil cans wherever the tall boy spawns, clear 3 more enemies, then keep last one alive to replace oil cans). You can set mines while the last enemy is alive like the other solution mentions, but with the oil cans allowing you to one shot both tall boys, and lots of bend time left, you shouldn't need them.
Step 10: At the start of round 12 you ought to have PLENTY of mana vials left and hopefully a health vial or 2 although you probably wont need them. Hit your bend time as soon as you see a tall boy spawn facing one of them at round start. Shoot his oil cans and IMMEDIATELY turn and shoot the oil cans at the other tall boy spawn. Now that both are cleared, hit another Bend Time (pop a mana vial if need be) and clear out the 2 'regular' enemies. Your last enemy will probably (and should) be the music box bastard. Take your time and savor the moment, then grenade him or whatever you like. Kill the merchant for kill #53, and watch as your well-earned achievement pops.
Landed on exactly 500,000/500,000gs with exactly 18500 achievements and exactly 500 games. All 100% including DLC. Was going hard the first half of January to reach that goal! Finished it on 1-19-2016. Final achievement: Completion Serenity in Nero.