Look inside the arch above the ice pond
Start from the ice pond and head uphill north/northeast to the stone arch. AttackOnMars places the cockroach high on a ledge inside the arch’s left side. It is a small object, rather than a statue with three target indicators.

Sources: AttackOnMars: unlock guide
Use buildables to reach the interaction
Prepare suitable props
The unlock guide uses a tower of props such as greenscreens. Obtain the needed buildables at the lodge prop shop before travelling to the arch.
Place a climbable route
Build toward the ledge inside the left side of the arch. The recorded keyboard build controls use left click to place,
Q/Eto rotate andXto cancel. These controls do not remove the need to unlock the prop first.Approach the cockroach
Climb until close enough to see the object’s interaction prompt. The task is completed by interacting, not by touching the arch or throwing snowballs at it.
Keep a return anchor near the approach if you expect falls. Use the controls table for your platform/input mapping; the exact number of props depends on your placement.
Sources: AttackOnMars: unlock guide · Volx: photographed input settings
Check the hat in your clothing choices
Confirm the Cockroach Hat unlock, then return to a clothing chest and select it. A hat icon in the video cover is a reward illustration, not proof that your account has acquired it.
If you were looking for a drinking reward rather than an arch pickup, the Hot Cocoa Hat guide covers that separate task. Other verified methods are in the hats directory.
Sources: AttackOnMars: unlock guide · FaeBee: achievement guide