Some background of the bike that I am working on, it has SRAM Apex RD, FD, and shifters.

I can't get it shift to the largest cog at the back. I tried to adjust the L low limit screw but it will shift to every single cogs but not the last one. Cable tension 'seems' fine to me but I am not 100% sure. Please advise

Sounds like either the shifter wasn't in the smallest cog position when the cable was attached to the derailleur or the cable needs more tension. Try shifting to the smallest cog then see if it will shift one more time. If so, loosen the fixing screw and remove all slack in the cable. Then add tension as needed to shift through all cogs.

It is important to have the chain on the smallest chainring and largest cog when adjusting the low limit screw.

If you pull on the cable by hand, can you get it to shift to the largest cog?

If so, then your limit screw is not the problem, it's a tension issue.

I pulled the cable by my hand and tighten it down, but it still wouldn't shift to the largest cog. Time to use the 3rd hand tool to pull it harder?

Loosen the L limit screw quite a bit and then pull the cable by hand. Be sure you're unscrewing the correct screw.

No, only a very small amount of tension is required to pull the cable across the entire range. So it's either your limit screw setting, or you have another issue like bent parts.

I think you misunderstood the advice. Leave the cable attached to your derailleur. Then pull the cable manually, find a spot where it is exposed, like on the downtube. From the highest gear (smallest cog), you should be able to manually pull the cable enough to reach all of the gears while moving the pedals (a bike stand works best for this, or have a friend raise the rear wheel into the air for you). If it doesn't reach the biggest cog, then either something is bent or your low limit is stopping you. Loosen the low limit a lot, and see if you can reach it. Remember to readjust the low limit before you ride the bike, so you do not risk throwing the chain and derailleur into the wheel and either crashing, or doing serious damage to the bike, or both.

Take close up pics and post if you want someone to guess whether something is bent.

Ah, I had misinterpreteted the OP's response and hadn't caught that he was simply retensioning the cable. Good catch.

OP: Once you check for full movement across the cogs by pulling by hand, as other posters said, loosen up the low limit screw and try again.

Additionally, on Apex RD's, if you stand behind the bike and look directly at the largest cog, try ( somewhat gently ) to move the RD so that the it is directly under the large cog. Check to ensure that the large cog, and the two pulleys ( gears ) on the RD are *exactly* lined up. That should give you perfect shifting into the large cog.

As a further sanity check - I presume you're not hearing any grinding when you try to move to the largest gear? If so, check and make sure that the upper pulley is not striking the large cog. If it is, you need to back off the 'B' adjustment screw so that there is a 6MM gap between the pulley and the cog.

And that makes me think - are you absolutely positive that you're using the low limit screw ( i.e, the upper one on the side of the derailler ) and not the B screw ( the one that comes out of the back of the RD )?