Basically anything but bit alpha will trigger software rendering, most image scaling or rotating also seems to do it. Drawing an image that has a different colour format is also a no no. Use createCompatableImage. Any AA also seems to make things really slow, so don't use that either.
For fonts with lwjgl, either TWL or Slick2d has things to manage bit mapped fonts.
Im dont fully agree that software rendering part, my oldie GF6200FX seems to handle all graphics2d commands, i dont have CPU load when increasing scale rotate or any other commands with bufferedimages or drawstrings, and all my bufferedimages are RGBA not compatibles ?