Question

For gaining high happiness, is levelling up a lot good or is fighting in a lot of battles?

Answer 1

Well, I don't really see the difference
To Level up you're going to need to battle, like it or not unless you have an endless supply of Rare Candy. Levelling up is one of the ways to increase happiness (Ranges from +2 to +6 depending on level), and that is done through battling normally. Soo.... both? :P
The point is, as long as you level up your Pokemon will gain happiness.

Comments

it also has soothe bell so it should evolve fast right as when i captured it its lv was 4 and now 35

Answer 2

I'd walk around with your Pokemon for happiness, but leveling up with Rare Candies will help, as fighting may make your Pokemon faint, which will decrease its happiness.