Those pesky purple monsters can be quite intimdating to new players, and occasionally not new players. The high damage they deal combined with high defense and HP makes them a challenge to deal with at the best of times. However, lots of them can be defeated surprisingly easily, when you have the right strategy. This guide will tell you how to kill purples using very low level characters.
Algos: Kaoka Parrej Ruins
Algos is a piece of cake for anyone with magic. He lives under a big gap in the floor past the 1st statue and to the left (east). When facing the gap from the statue side, head to the leftmost side of the gap and walk off the edge. You should fall onto a small ledge. From here, you can drop ice bursts, holy lights, fire arrow &c on top of him, completely free from harm. You can even camp when your MP runs out.
Now that there has been the update with bridges, most "big people" can't use this strategy any more. There is however an alternative. You can fire "arrows" at Algos from the top ledge without the need to jump down.
Greed Eater: Deltis Keep
Another easy one for mages, simply hurl an arrow &c and run. Fast. If you're really lucky, it will get caught on the flame trap and take even more damage. For non-casters, try attracting its attention and getting it caught on the flame trap. It'll take a while, but should be relatively safe to do. Any character on a moderate level (20+) should be able to take care of it without too any difficulty.
Aria Tsitsi Fly: Aria Reservoir
Again, recommended for magic users, but traps will work for this one. The Aria Tsitsi Fly can appear in 2 places that I now of: just past the first statue on the second floor, going straight ahead and to the left and in the dead-end of the sewer going from the first to second statues on the same floor. Luring this is tricky. You need to hit the fly with a spell, and then RUN to the safety of those small corridors leading to and from the sewer part. Hopefully, the fly will follow you and not kill you. Once you are safely inside the corridor, the fly will attempt to follow you. However, it will get stuck near the high end of the corridor and be unable to move. At this stage, you are free to blast it with spells.
After a while, it will seemingly disappear. DON'T leave your position (unless you're a thief). The fly has simply done what I call a soft respawn, ie it respawns, but with HP and Hate at the same levels. This means it's going to come buzzing all the way back to you in your corridor... and get stuck again. Now hurl spells at it again. It soft respawns, comes back, you cast spells on it, soft respawns, comes back, you cast spells on it &c. Trap thieves can place traps near the entrance which will be triggered as it comes back. DO NOT go into stealth, this removes the hate and you will have to lure it again.
Daniel-san: Golden Dragon Ruins
Daniel-San is ssssllllooowww. Anyone can take him out without too much difficulty, provided they can do more than 1 damage to him at a time. Priests with Holy Light will find it easiest. Daniel-san is located either before the ladder leading up to the first statue on the second floor, or just after the second statue. Fighters will prefer him being in the latter location because it has a guardian statue nearby.
Since he is just so slow, just hurl spells/drop traps in front of him; you have plenty of time to get out of his way. If you need healing for MP, climb on top of those handy ledges. He can't (usually) reach you there, but stay away from the edges. Occasionally he soft respawns, but he'll come back fairly quickly.
Million Star: Temple of Oblivion
His large size works against him. In either of his two spawn locations, there are some stairs leading down. About half the time he will get stuck while going down these stairs. From there, any ranged attack can take care of him easily.
Levi Machine: Old Sewers
This one needs a party, preferably a fighter with high def (priests work too) and a spellcaster. Levi Machine always appears in the Balboa Family's Territory, on the far west side after the guardian statue. He has friends. Lots of friends. This is the main challenge with him.
The fighter needs to lure Levi all the way back to that hole directly south of the guardian statue, hopefully avoiding as many of the other monster on the way as possible. Then, jump down the hole. Levi (and co.) will jump down there after you. Meanwhile, the spellcaster can come out and hurl spells at him from the safety of High Up. The fighter will probably need to run around screaming down there to keep Levi interested.
Man Eater: Old Sewers
This spider barely even needs a guide. If you can get to him, chances are you can kill him. It's a good idea to hug the wall as you approach him, because while he isn't hard, his friends nearby are...
An easy (but painful) way to do this is to just whack him until he kills you then go back and revive. He has very low defense (for a purple) and equally low HP so you will probably only need to die about 5 times maximum before he dies.
Curse: Old Sewers
Attract his attention somehow, then hurry back down the ramp to the sewers. Wait near the bottom at the sewer entrance, then go back up. He should hopefully have gotten stuck, leaving you safe to whack him. After a little bit, he will soft respawn. If you still have agro when he comes back, wait near the bottom of the ramp for about 7 seconds to allow him to get stuck again, whack, soft respawn and repeat. He does have fairly high HP, so this may take some time.
Spiral Mixer: Underground Dragoon Ruins
Surprisingly easy, once you get in position. Climb up onto the third step on the stairs near where he lives. Attract his attention somehow, and wait until he gets stuck as he tries to reach you. Then you are free to hack him to pieces until he soft respawns. Repeat until dead. This can theoretically be done by any class.
Most other purples are in awkward places that don't allow for easy picking off. However, even a group of just two mages with Ice Burst can easily kill most purples, provided there aren't any other monsters around. With three mages, the ferocious purple will be unable to do anything more than glare at you. The only exception of course being Sollguva in Chikor Castle. He is also the only exception to the "spellcasters only" in purple hunting that I know of.
Notes on purples
Usually, purples have lower magic defense than physical defense. A level 3 mage can kill Algos, for example, but even higher level fighters can struggle to do much damage to him.
Most of the magic defense of purples isn't actually in magic defense. I suspect that it is actually in Dark elemental affinity. This basically means that your standard fire, earth, water and wind spells will do nothing until you reach some threshold value. On the other hand, Light element spells (the only one of which is Holy Light), will bypass all that, and in fact even do MORE damage. See, Holy Light isn't such a useless spell after all, is it?
If your fighter is doing 1 damage to a purple, stop hitting it with a weapon. You'll do just as much damage with your fists, and your fists don't break. Daniel-San is immune to the instant kill of Holy Light (if he isn't, it's probably <1% chance), which probably means that if at some point in the future instant kills become possible on any monster, all purples will be immune to them.
Got a strategy for killing purples? Let me know and I'll include it above. I have only just beaten floor 1 of OS, so I do not as of yet have a method of killing purples past that point.