Working on my Nids.

In cougar form, you just have to spam her abilities, and of course you'll need different items to be more efficient, like a trinity force would be good. I don't play Nidalee in cougar form that much, I just use that for running away.

 

Yea, I mainly use cougar form to escape from a team fight as well. But I also use it to chase an enemy down. Whenever they are pretty low on HP, I tend to run them down with cougar form and press Q then E to inflict some damage to them, and then the moment I sprint once more towards them, I immediately change from cougar back to human form and pop my Q right there and then. If the Q hits the enemy, it usually gives me the kill. Make sure you estimate the damage you do to them so you can get that kill. If they have over half of HP left then I do not think the entire combo will be able to kill them.

 

Cougar form isn't hte best for fights tbh. As everyone has said, its the mobility that you really want from going into cougar, either to chase down or run away. Most Nids I see will run around the map as cougar, and change to human to throw the spear.

I would just keep to the spear throwing from a distance. It deals so much damage, and if you hit their adc or ap carry, then it puts the whole enemy team at a disadvantage of you go into a teamfight. It usually forces someone to return to base, giving your team a 5v4 advantage.