In 35 moves hatch 6 eggs. Now the only way to hatch these eggs are through special gift explosions (and boosters if you want to be cheeky). The two grids surrounding the birds are wide enough to unwrap all special gift combinations. So take your time to scan for those combinations.
The grid will conveniently push the eggs along a straight line, giving you ample time to create enough striped gifts and match them when an egg is in your scopes. Be patient with the grid barrier though, it might take some time on those last couple of eggs.