Get Guitar Pro (Tab software), tab out or download whatever it is you want to play and use the speed trainer. Basically just highlight the part you want to loop, and the speed trainer will loop it for you and increase it a little bit each loop. This did wonders for me back when I was learning how to shred. I just loaded up all the modes of the major scale and harmonic/melodic minor, then used the speed trainer to run through them until my speed built up. As soon as the speed gets too fast that you start to play sloppy, reset the speed trainer and start from the slow speed again.
I think lessons are good for theory and learning new tricks, but for something like shredding or building speed; you just have to put in the hard, repetitive practice.
Also maybe just try to build speed on one string playing 3 notes of a scale; (5-6-8-6:|) for example. Once you build the speed on one string you can try connecting it to a second string.
I can help you out on Skype if you want. Been teaching for 12 years and may be able to help you refine your technique and make a practice plan. 225bpm is possible, but it is likely to take a long time to develop this speed with a relaxed technique (depending on the level you are currently at and any bad habits you have picked up)