Quick knife attacks and fast firing of arrows can be a huge help in whittling down the enemy's health. As the platform starts tilting, run to the other side and jump up to avoid the ground attack, then immediately run back towards the boss.
When he leaps in the air, dodge roll forward. If you time it right, you should avoid his ground attack and be directly on the boss so you can get in a few swings. When he roars and starts his swing animation, dodge roll away or run to the other side of the platform to avoid his arms.
During the phase when the ice walls land, keep in mind that they don't actually form and cause damage until a split second after the falling animation. You can use this to your advantage to quickly get out of the way.
In the next phase, pay attention for randomly-appearing skulls so you can dodge the incoming icicle attacks. However, don't forget you can actually smash the icicles in the air before they fire at you. If you stay very close to the boss, you can jump up and hit both the icicle and the Tundra Lord at the same time.
In the final phase of the fight, The Tundra Lord floats in the air while icicles fall straight down from the sky. In this section, you'll need to master jumping either slightly to the left or slightly to the right of each icicle to avoid getting hit but also giving yourself a window to strike the boss.
It's actually easier to stay in a fairly tight area rather than trying to run around to avoid the falling debris.