Horizon Zero Dawn is great, but I had a hard time beating the Behemoth and decided to share the strategy I formulated. I've also attached a video guide (starts 20:48) showing the death arena as that was a constricted and most tough area to battle a Behemoth. This is mainly to add a visual aid and details on how to beat Behemoths will be described in text. The key goal when taking on the Behemoth is to halt its momentum, the thing is constantly moving and are horrible to battle with precision arrows. I would also say that it's essential to have a strong bow, a quick bow and one from an earlier main quest that allows you to tie down enemies. There are a ton of resources around the arena as well with wire from fallen machines and health herbs being your best friends here.
Rolling is also important when dodging attacks and you'll switch between doing that with shooting. To start it off, when you get your weapons gather a sense of surrounding and stay towards the edges. When it comes towards you shoot a single tie down shot to halt its movement. Fire away at it with some fast arrows until it breaks free and continue to do so when the opportunity presents itself . Eventually it gets fatigued to some degree and that's when you unleash the stronger bow for better damage. With each arrow, the main goal is to hit the energy cores on its face as those basically kill it (deal most critical hits) and then finish the beast off with body shots. It does retain most of its strength through the attacks on its face, but once those are really damaged the creature will limp for an easy kill. Remember that it's all attack so you need to keep halting its momentum and take chances only when presented as it can insta-kill at anytime.
Our Horizon Zero Dawn Hub
Read our Horizon Zero Dawn Review