For this you need a Soul Reflector, and you need a couple things to make one.
The first is an ice crystal, you get these by having the signet status effect (many gate guards in your home nation can provide this) and killing monsters in base game areas that provide experience. If you've been running around with signet on you no doubt have plenty of these, if not you should find some in the auction house for pretty cheap. 1k for 12 on my server, though yours may vary. Getting them from the AH will be much quicker.
The next is a soul plate, and for that you actually need 2 things, an empty soul plate and a Soultrapper. Both of these are acquired from a merchant in The Pit in Aht Urhgan Whitegate, but you need special currency. Jettons are what you need, and there are 2 ways to do this. You can get sanction from Asrahd at I-8 in AU Whitegate and kill enemies that give experience, use the imperial standing to get imperial pieces, and trade them for Jetton, or just buy the imperial pieces from the AH. You only need 4 Jetton, so an Imperial Silver Piece from the AH is good enough, and it's only 5k gil on my server. If you want a Soultrapper 2000 (which might be better than the Soultrapper, no one seems to know) you'll need 500 Jetton. You'll need at least 3 Imperial Gold Pieces for that, and they are 19k gil each on my server, so eh.
It seems you can buy them for gil if you're far enough along in the Shantotto quest line, but I try to avoid doing more quests than I need to, since FFXI's quest structure sucks. Once you've finished the second quest on the Aht Urhgan questline (you need to do this questline for an achievement eventually anyway) you can get sanction.
Either way, once you have the proper imperial pieces head to Zandjarl in The Pit (the entrance to the pit is marked on the AU Whitegate map, the entrance is in the southeast part of the map) and then trade the pieces to him. Then buy the soultrapper and soul plates from the 2 point category (the soultrapper 2000 is in the 500 point category FYI).
Alright, we're in the home stretch now. Next we need to use these 2 tools to capture a monster image. Equip the soultrapper into the ranged slot, and the soul plates in the ammo spot. Enter Bhaflau Thickets (west out of Whitegate to Al Zhabi, the exit to BT is northwest of you on the map, clearly marked).
Walk up to one of the spiders and target it, go to items, and then use the soultrapper on it until it successfully gets an image. My soultrapper 2000 got it first try. This does not appear to draw aggro, but you may want to summon a trust or two just in case. Once you have it go back to The Pit and talk to Abhram (from where you enter, she's a bit forward and to the right). Trade your ice crystal and the soul plate with an image (the description will say it has a monster on it) and you'll get a soul reflector for 1 Jetton.
Now trade your soul reflector to Kadjayhal next to Abhram to get an official one. As with all achievements in this game, you'll need to talk to a traveling bard to unlock the achievement. Go here : http://ffxiclopedia.wikia.com/wiki/Traveling_Bard
to find one that you can get to.