When we were in Cát Bà Island, we didn't just check out the water. We also checked out the land. So the day after our day trip on a boat, we did a day trip on land. We rented a taxi as well as a guide, who took us to Cát Bà National Park. This was actually a strenuous hike, and involved a lot of sweaty moments, as well as a shirtless hike to the top of a rock.
See, this was perhaps the first time I was trekking in a tropical environment. I found it surprising that I started sweating quite a lot, compared to my other treks. And since it was humid, sweat doesn't dry off your body. It just stays there and sticks there. It's not the most comfortable experience. So yeah at some point, it became easier to just take my shirt off and hike as is.
Cát Bà National Park is actually a very green area, with plenty of plants and other natural elements. The trail is not the easiest, so be prepared, and make sure you have plenty of water. The views at the top (there's an observatory at the end of the trail) are amazing.
After finishing the trek to the observatory, we then went to the Trung Trang Cave. It's a short drive from the main entrance of the national park, and it easy to miss. The cave isn't the most spectacular, but nevertheless is worth checking out. There's a series of long staircases to get to the entrance, and inside is a very sanitised path, so no mud nor guano, so it's definitely a walk in the park.
This pair of activities can easily fill half a day, so if you want to check out the interior of Cát Bà Island, then this is a possible thing to consider.