First and foremost - get a pre-emptitive strike by approaching from behind. Pasarans can move through walls but they are still relatively slow in their floating. Getting the first turn is crucial for all kinds of setup.
The first stratum Pasarans have Run Away, which is a leg skill. If you bind their legs, they cannot run away, and you'll be free to beat on them. To your convenience, one of the better leg-binding moves is an early skill for the Ninja, who naturally tends to be fast and can usually pull it off before it runs away (should you have failed to land the bind in your free turn). The Pasaran has 120 HP that you'll need to break through.
This is just stalling for time, though - you'll need to make sure you can do all that damage. You can improve stalling by adding additional effects like Paralyze for its chance, Sleep for its full disable and extra damage, and Stun if you can land it. The Lion, if used properly, is exceptionally potent for a combination of Stun, Paralyze, and high damage. Also keep in mind Limit Skills that activate at the start of the turn - you can use these to clutch victory right when your stalling is out.
Each of the first five strata will have its own kinds of adorable Pasarans that may appear. They each have their own entry in the Monstrous Codex. Killing a Pasaran is worth a ton of experience. They're very, very nice. The lower the stratum, the better the rewards. However, their tricks to hose you and your rewards differ with each one. I've included these in spoilers so that you can access them at your discretion - they also include HP values so you can figure whether your attack power will be great enough.
Looks to its left and has 220 HP. And it explodes! This harms all of your party and also destroys it for no reward. You need to bind its head to prevent this.
Looks to its right and has 350 HP. Explodes or runs away! You need to either be really really quick, or need to pull off both binds.
Has its arms raised, hee, and has 480 HP. In addition to possibly exploding or running away, it also has an ability where it will put its arms down - this transforms it back into the first stratum Pasaran, complete with pathetic rewards! Arm bind will prevent that. They tend to prioritize doing this over exploding or running away, because they're mean like that.
Here's the crazy one. There are actually three kinds, but you only encounter the first directly. All three versions have 650 HP.
Blue Pasarans are happy and explode, but more relevantly, if they are hit with a Fire, Cold, or Volt attack, they will multiply into a new one! The color is based on the element, you obviously get more Blue if you use Cold attacks. Multiply is essential for maximizing your gains, and for this reason getting first strike is even more important. Be careful, though, as mistiming or falling short can end up with 5 Pasarans exploding in one turn, which can deny your party's life instead of just rewards of battle.
Red Pasarans are worth the most experience of all Pasarans, and are made from Fire attacks. These angry guys possess the ability to both explode for major damage, hit all allies for fire damage (but they stick around), or they can lower their arms like the fourth stratum Pasarans. Kill them quick.
Gold Pasarans are the only ones with a drop - they can drop an item that sells for a lot of gold. They multiply from Volt attacks. However, these sleepyheads have an attack, Unload, that hits all of you for lightning damage and destroys their drop. So you have to kill them before they pull this off. I have, alas, forgotten which bind stops Unload but at this point it's a better idea to just kill them immediately, ideally by Limit skill.