You're going to need to be quite creative with this one, but it can be done.
The good news is, if you manage to get a green slmie to hurt you, it seems to do a lot of damage. At least 5 hearts worth.
Here's the setup and explanation:
First of, you need a way to make the green slime move. Almost no enemy can hurt you, unless they move into you. Scroll of Fear will make the slime move without hurthing it.
Secondly, you need to move to have the slime move towards you. There are a couple of ways to do this.
Scenario A: Confuse
When the slime gets confused, it will move in the opposite directions. This means, in stead of moving away from you (under the Fear effect), it moves towards you. There are a couple of ways to cause confuse
The most reliable way to get a slime confused, is to play Dove (unlocked by beating Zone 2.) Her weapon is the Flower that causes Confuse on all the enemies hit. Of course, playing Dove makes finding the Scroll of Fear less likely, as shops will only carry two items instead of three.
Alternatively, you need a Confuse Trap. The Feared Slime will need to move onto this trap at which point it will swiftly change direction and berge right into you. (May not be viable as Confuse Traps and Green Slimes don't seem to spawn on same floors.)
With all this done, you only need to stand still and let the green, slimy nature take its course.
Scenario B: Bounces (highly unlikely)
If you're really lucky, you'll find the bounce traps in a configuration that will bounce the frightened slime on you. These may be rather rare, tough, as you need the slime to bounce one square behind its original position.
I've tested this in the level editor mode and these both work reliably. However, it seems you can't get the achievement this way. You'll just have to play the game normaly and hope to get what you need.
Who knows, maybe someone will find a seed that will have these setups easily attainable. According to the developer, you can't unlock achievements with seeded runs.
Since this hasn't got any answer, I'll supply with the generic wiki search
What it says about gold weapons :
Monsters drop 1 additional base gold (is affected by the the Groove Chain multiplier). Makes monsters in boss fights drop 1 gold. Deals 999 damage on the beat after collecting any amount of gold.
What it says about the golden ring :
Killed enemies drop 1 additional gold (is not affected by the Groove Chain multiplier).
If you are lucky enough to find the ring of becoming and transmute it (transmogrifier NPC or transmute spell/scroll), you can have access to the most valuable ring of the game, the ring of Wonder
Here is one of the bonuses attributed to the player wearing this ring :
Killed enemies drop 2 additional gold (is not affected by the Groove Chain multiplier).
The two pieces of equipment stack up the gold, and having only the gold weapon is better than having only the gold ring, due to a groove multiplier influence.
GM = groove multiplier
BD = Base drop of the ennemy
drops :
no gold equipement : GM * BD
gold ring : GM * BD + 1
gold weapon : GM * (BD + 1 )
both : GM * (BD + 1 ) + 1
EXAMPLES :
Green slime, x4, both pieces
4 * (1+1) + 1 = 9
Green dragon, x3, both pieces
3 * (10 + 1) + 1 = 34
EXCEPTION : With both pieces of equipement, the boss minions (any mob inside the boss room except the boss) only drop 1 coin due to the gold weapon's attribute. Having the ring won't make them drop a coin.
Also, in the case of death metal's summons, the number of 1-coin drops have a limit.
Best Answer
New Answer: YES, and it's not difficult to do now.
Note: Look in the edit history to see the old answers.
Since Necrodancer's release, there is now an NPC available called the "Weapommaster" that will swap out your weapons for training. You need to buy him for 400 gold from Zone 2.