You'll need a legitimately caught shiny pokémon, meaning not chained or bred. It has to be a regular shiny. Then you're going to have to use X-Act and Jump's PID applet. They're from Smogon, BTW. Or, you could ask someone here. One of the most helpful people I know, World King, would probably be happy to help you so just ask him.
By the way, RNG Reporter (also found on Smogon) is a program that will let you work out your SID from chained shinies, too. You'll need to chain multiples though (around three or four), which isn't that hard if you're even half-decent. You'll need the latest version to do this (7.00).
Oh, and full 31s with breeding are actually pretty easy if you know exactly what you're doing. In the past few days, I've bred about 5 31/x/31/31/31/31 Pokemon, without an AR (and definitely not playing it 24/7). If I was going for a mixed sweeper, then I could probably do a similar amount of full 31s in the same amount of time. The only problem I have is that I don't currently have reliable computer access, so I can't actually check their IVs... I know at least two of them are effectively flawless, though (Roselia and Porygon), and suspect 3 more are - Chansey, Piplup, and Wurmple (don't ask :P). However, I used RNG Reporter to help; without it, it would take much longer, but it's still possible if you have good parents.
If you're not breeding, and don't know how to (or don't want to) manipulate the RNG, then it's much harder; the chances of finding a flawless wild Pokemon are exactly 3/2147483648 (about 1 in 700 million). Again, if you use RNG Reporter, then it's much, much easier (I caught my brother a 31/31/31/31/31/31 Palkia in just a couple of hours).
By the way, 25/20/26/28/30/27 is no easier to get than 31/31/31/31/31/31; all IV combinations are equally hard to get. However, obviously getting
at least 25/20/26/28/30/27 is going to be a lot easier. You'd probably want 31 Speed at least, though; Speed is the most important stat to have 31 in (since one point less can mean you go after your opponent, giving them an extra attack, while a point in another stat will just have a very small effect on damage). My own Gengar is 31/10/30/31/31/31, but that's because I'm a perfectionist.