Starting a Large Grid
Begin with the regions that stretch along a single row or column, then with the smallest ones: on an 8x8 grid, a region of four cells in an L or a square leaves only a few places for its star, and the cells that touch all of them can be crossed out at once.
Group Reasoning at Medium and Hard
The larger the grid, the more useful groups become: two regions inside two rows, or three regions inside three columns. At Hard, when no group helps, try a star in the most crowded region and follow its consequences until a region runs out of cells.
From Screen to Paper
Solving on paper lets you keep notes: dots for empty cells, small marks for the cells a region still has. The 8x8 grids are large on the page, so these marks stay clear.