I've not taken the entire T/T out of the 225, just replaced the T/T motor. However, I believe that you can remove it without removing the engine.
You will need an overhead beam or a strong branch of a tree. Loosen the manual release screw on the T/T. Raise the engine to maximum height. I've used a come-a-long and a tow strap, but anything that will support the engine's leg and will attach the the hook on the come-a-long should work. You can use a step ladder as an extra support. Alternatively, you can fabricate a sturdy ground brace. Just remember that you're fooling around with a 600+ lb. engine. If done properly, the transom will be carrying most of that weight.
Disconnect the electrical connectors to the T/T motor and the trim indicator and snake them back out of the upper cowling on the engine.
Remove the two E clips on the upper pin where the T/T attaches to the engine, then carefully punch out the pin, being careful not to damage the two bushings in there. Then push down the tilt arm all the way. See item #23 at:
http://www.boats.net/parts/search/Honda/Outboard Engine/2005/BF225A5 XA/POWER TRIM-TILT/parts.html
Remove the long bolt through the lower part of the mechanism.
Remove either the left side or the right side bolts that attach the engine bracket to the transom. Loosen the bolts on the opposite side,
but don't remove them.
Gently pry apart the bottom of the stern bracket so that it just clears the collar holding the T/T mechanism. See item # 25 at:
http://www.boats.net/parts/search/H...225A5 XA/STERN BRACKET SWIVEL CASE/parts.html
Be sure to have someone holding the T/T mechanism while doing this, because it will fall out as soon as it clears that collar.
When re-installing, be sure to reseal the through bolts going in to the transom. I typically use 3M 4200. Also, don't forget re-installing the two wave washers.