From the map start, go upstairs to the west. North of the rocket launcher, you will find a piece of rock with a different texture. Push that part of the wall, it will lower, granting you access to a teleporter. The destination is the ledge nearby (Sector 72), where you find a Megasphere and a box of shells.
After crossing the cave near the lava pit in the north west, walk to the western ledge and look into the north. You will see a lower ledge. Jump down there and follow it to the platform (Sector 186) containing a Megasphere. Drop down to the teleporter to get back to the cave entry in the north.
After leaving the cave to the south and continuing your way, you will arrive at a platform where [14 Spectres on easy skill, 8 Arachnotrons on medium skill, 14 Arachnotrons on hard skill] as well as a Megasphere await you. South of that platform are some stairs leading up to a higher platform. In the south between the 4th and the 5th stair, drop down to the south. You should land on a ledge (Sector 189) and get an invulnerability sphere. Use the teleporter nearby to get back to the stairs.
Continue your way up the stairs you have been teleported on after collecting secret 5. On the upper playtform you will find a switch. Behind that switch is a BFG-9000. (Sector 106)
Activating the switch mentioned in secret 4 opens the cave in the west north west of you. After crossing that cave, climb up some stairs, move on to the west until you reach a switch. Either, drop down into the lava pit and go south to reach the teleporter. Or even better, activate the switch to open the next cave, cross it and jump down through the first opening to the aforementioned lava pit to the north. You should almost land on the teleporter. Either way, the teleporter destination is a ledge in the lava pit in the cave before (Sector 134) where you get another invulnerability sphere. Dropping down into the lava pit the first time will teleport you back near to the last switch. Dropping down into the lava pit the second time: quickly run to the first window to your right and push the wall to activate a lift to get back to the cave.