For example Tamiyo, the Moon Sage. Can I use the -8 ability even though she only has 4 loyalty? I understand it would kill her. Or would I have to get 8 loyalty first with the +1 ability?
Wizard's wording on the matter is thus:
606.5. A loyalty ability with a negative loyalty cost can't be activated unless the permanent has at least that many loyalty counters on it
It doesn't specify how those counters get there. It could be through +X abilities, proliferate, or even cool things like Doubling Season. But they must exist on the planeswalker in order to pay the cost.
First things first - planeswalkers don't have "life", they have "loyalty counters".
Unfortunately (or fortunately, depending on the side of the table you're sitting on), you can't play an ability with a negative loyalty cost unless the planeswalker has at least that many loyalty counters on it.
See here for this and other official rules for planeswalkers in Magic.
This works in the same way as casting a spell/ Activating an ability. In order to do so you must pay its cost. If you don't have the manna for the cost, you cannot cast the spell.
The abilities of a Planeswalker require the costs next to them to use them. Even the +1 abilities are a cost. (However, it would be very rare/ impossible to be unable to pay that cost.) -1, -2, -10, etc... costs act the same way but you would require that specific amount of loyalty counters or higher to use them:
606.5. A loyalty ability with a negative loyalty cost can't be activated unless the permanent has at least that many loyalty counters on it.
Think of it this way: No store that's selling a 5 dollar sandwich is going to accept 2.50. or a 1.00 sandwich for .50 cents. When a Planeswalker ability says "-2' do this action" you need to pay 2 loyalty, no ifs, ands, or buts. If you have 1 loyalty on the walker and you want to use the -2, no dice, you need at least 2 loyalty since the minus two is the cost of activation. So if you want to activate a minus ability but lack the funds, you need to find some way to get that loyalty up, whether it be activating a +(#) ability or blinking/flickering the walker itself to reset to base loyalty.