Brotato

This achievement can be a little tricky since you'll need to be set up properly. Namely, you need to have enough trees spawn AND not kill them (purposely or accidentally). Here are things you can/need to do to make this achievement easier to get:
 

• Play as Explorer. This character gives you a bigger arena, meaning easier to avoid trees so you don't kill them, and this character gets more tree spawns. WAY more.
• Play with Melee weapons. This is important so you aren't accidentally hitting trees far away unintentionally
• DO NOT get any turrets from the shop, nor Pocket Factory. Your turrets will automatically target trees if no enemies are nearby. Pocket Factory makes those dead trees spawn turrets, which snowballs into making this achievement impossible with those items
• Look for the item that makes "more trees spawn." If you can get one, two, or even three of these on a run, you'll get plenty of tree spawns
• Avoid the item that makes trees die in one hit
• Wait to go for this until later waves that are longer, so there is more time for trees to spawn
• Keep an eye on the arena for the green Xs, which is where the trees are about to spawn, and stay away from them

You will definitely accidentally kill some trees, but with any luck, you can stay in a corner or against the edge of the arena and avoid killing trees so enough spawn and stay alive for when the wave ends. This achievement will unlock if a wave ends with ten trees left alive.

My experience was that, playing as Explorer makes a ton of trees spawn by default. I didn't need any items to increase tree spawns. I just kept melee weapons only and avoided turrets so I wouldn't kill trees. I got this achievement on Wave 4 as Explorer, because that's when waves were long enough for enough trees to spawn. Keep your distance and this should be easy to do intentionally as Explorer later too, with longer waves.