The first step is to solve one pair of oppposite cells using the instructions for the Starter Hypercube and then move them to the center and outside (the non-visible 4th dimension). The second pair of cells is solved the same way except that the quarter-twists (U or U' to front, right, back or left cells) are no longer allowed because those would mess up the solved cells. After solving the second pair of cells turn the whole hypercube so they are on the right and left.

To solve the last two cell pairs use Sequence 4C-C2 which fixes the four misplaced cubies on the front cell as can be seen on the following image (the four misplaced cubies on bottom cell also get fixed). Sequence 4C-C1 can not be used at this point because it also swaps another pair of cubies on the left cell which up until now did not affect any of the already solved cells (this can be seen by doing the reverse sequence on a solved hypercube).

If the above setup can not be made with half-twists then just match three of the four locations (on front cell) which will result in two of them getting fixed (three fixed less one misplaced from bottom cell equals net of two fixed). When there are only two misplaced cubies remaining then make the usual setup (shown below) and complete the corner solution with Sequence 4C-C3 which has 26 moves (hence the reason you only want to use it once as opposed to using it several times to solve two misplaced cubies at a time).