For zips to work correctly on PC, you need to run the game at 62fps, which is the default framerate without v-sync. If it's running at 60fps, you need to disable v-sync. Disable it in the game's launcher, and make sure it's not forced on by any third-party programs like Nvidia Control Panel.
You also want PhysX off, and DirectX 11 Features and Tessellation off. PhysX generally creates lag, and I have no idea what DX11 does in the game, or how it affects the speedrun, but apparently it's best to have it off.

The following discoveries and route changes have been made since this video was uploaded:
This list may not be comprehensive, and is subject to change.
Slightly faster Bruce Wayne jump
Assembly skip - fastest version (currently no dedicated video)
Ground Takedown Cancels
Grundy Reloads
Faster Freeze fight on Easy
Partial Trials Skip
Bell Tower Skip (there is a faster glide, but no video of it. watch a run, I guess)
Steel Mill 2 Skip

3:05 - Intro Fight skip/Dumpster Dive - More details here:
4:50 - Courthouse
6:34 - Church
11:16 - Steel Mill
14:14 - Cancelling Doors with Gadgets other than the REC
18:05 - Standing Storage
19:53 - Mr. Hammer skip
21:53 - GCPD
24:49 - Corner Zips - More details here:
26:28 - First Upgrades - Bat Swarm & Multi-Ground Takedown
28:04 - Museum 1
29:39 - Failing Jammer Cancels
31:07 - Actually Cancelling Jammers
31:29 - Second Jammer Zip
33:23 - REC Jumps/Super Jumps
36:17 - Third Jammer Zip/Subway Zip & Gargoyle Storage
40:00 - Museum 2
41:36 - Dino skip - The single zip method I mention is now considered standard and is explained here (Enable Subtitles):
46:36 - Gel Warping
54:36 - Grundy
58:17 - Corner Zip after Museum - Console Alternative:
1:03:08 - Dead Parents skip
1:09:20 - Ra's Gliding
1:13:11 - Ra's Fight
1:16:47 - Zip after Ra's & Backup Strat
1:21:06 - Second Upgrades - Critical Strikes & Combo Boost
1:22:24 - Mr. Freeze
1:24:19 - Vicki Vale cutscene skip
1:25:18 - Upgrade - Batclaw Disarm
1:25:50 - Stacy skip - If you fail the cancel, you need to reload checkpoint once you're through the door. Reloading checkpoint loses gargoyle storage, so you need to do this:
1:31:44 - Fun House
1:35:10 - Protocol 10 skip - Backup strat:
1:43:30 - Clayface

cojo's tutorial: