At the fourth level there is a side mission called Snack Attack. Early on I think this is the best way to earn the skill points.
You seem to be able to run through it as much as you want to.
For my first run I got two skill points, then I saw it scored on kills, items collected and did it again picking up everything, kills way more than required, emptying guns just because...
For each run through I got three skill points. After the level you can then assign the skill points into the health slots.
Also keep in mind if you start New Game Plus after you complete mission 10, your stats will carry over and will make it easier to get more xp as you will received 2x the points.