To end the rainfall, you need to help the Weather Wizard get into the lighthouse, which in turn requires you to rescue Raph the lighthouse keeper, who has been kidnapped by a monster called the Tralü.
If you haven't already, in Twinsen's house, use the action key on the drawer in the bedroom to retrieve a key which can be used on the door next to it. In this back room, you will find your Holomap and Magic Ball (the latter being your primary weapon in the game).
Using the directions above, exit Twinsen's house and proceed to Mrs Bloop's Private Museum. You will need to enter the building on the upper floor via the window to gain access to your Ancestral Tunic, which will be important later in this guide.
Heading up towards the cliffs, you can access the Tralü's cave either via another cave which contains a large spider or you can forgo this by carefully jumping off the cliffside beside the Weather Wizard's tent onto the cliff path below.
In the first section of the cave, you will stumble upon Raph, who is trapped behind a locked door. Heading in the opposite direction, you will be presented with a locked gate and a lever on the other side of an obstacle:
To open the door, switch to "Discreet" mode and throw your magic ball, which will arch over the obstacle and activate the switch to open the door (if you do not have your tunic you will not be able to do this as you are unable to store magic to power the magic ball).
In the second area of the cave, before you climb the broken ladder, you will need to activate a second switch, which can be found at the end of the lower section of the
area. If you have trouble getting past the fireballs, changing to "Discreet" mode will cause the fireballs to arch over Twinsen. Once you reach the switch, as before, change to "Discreet" to arch your magic ball upwards to hit the switch and open the adjacent gate.
In the third area of the cave, you will encounter two "mini" Tralü monsters in separate arenas which both drop keys to open nearby gates.
In the final area of the cave, you will encounter the Tralü - the first boss of this game. The Tralü uses fast attacks, so I recommend using punching via your "Aggressive" behaviour mode instead of throwing your magic ball. If you find yourself stuck in the animation while getting hurt, quickly change behaviour modes to cancel the animation and resume fighting. Once the boss is defeated, you can rescue Raph in his prison cell.
Eventually you will play as Twinsen and Zoé together. Walk to the lighthouse and interact with the Weather Wizard, which will trigger a cutscene. Once the rain clears, the achievement will pop.