This is mostly a dynamic range problem: the contrast between sunlit patches and shade often exceeds what a single exposure can capture cleanly.

Best approach:

• Shoot RAW so you have more latitude to recover highlights and lift shadows.
• In post, reduce highlights, raise shadows, and fine-tune the black/white points and curves so you avoid excessive pure white or pure black.
• If needed, use local adjustments (brush/dodge & burn) on the brightest and darkest areas.
• Be cautious with contrast, clarity, and saturation—woodland greens can quickly look unnatural.

In the field:

• Softer light helps a lot. Try cloudy conditions or shoot earlier/later rather than near midday.
• If your camera offers contrast control, lowering in-camera contrast can help for JPEGs.
• HDR/exposure blending can help in very high-contrast scenes, though moving leaves/branches may cause ghosting.

A wider aperture or higher ISO won’t solve the core issue by themselves; they affect depth of field and sensitivity, not scene contrast. The biggest improvements usually come from better light, RAW capture, and careful post-processing.