Taken directly from Discord:

1. definitely try different paths. Normally the orange or copper enemies allow you to choose your path. Some paths are obviously shorter than others, and some are pretty close. I think my fastest run are the best paths, but it's hard to say on some. At the end of level 2-1, the barrels on the side are the way you choose which side you end up on on the train in the next level.
2. Headshots kill the fastest. Best case is you get headshots constantly so you don't waste any time shooting an enemy 2 -3 times to force the game to move on. You'll notice some sequences take longer to end if you only get an arm or leg shot. Plus limiting your reloads and using your entire clip as much as possible will save you small amounts of time throughout the game.
3. There are many enemies that the game gives you a chance to catch before they pop out entirely. Try to memorize those spots so you can kill them as quickly as possible. If the head isn't visible at first, pump a few extra to ensure a quick kill.
4. When it comes to grenades, sometimes it's best to use your clip on the enemies, then plan your reload around dodging the grenade.
5. Some people use RTA timing to gauge how quick their run is. I find this annoying so try to remember what your times are for each level so you have a good idea if you're on a good speed.
6. The level 2 boss with the gatling gun and giant rocket can be done really quickly if done perfectly. There are parts where shooting him doesn't matter/count so try to keep your shots accurate and reload when cannot hit him.