Cavein breach of a 2 level aquifer useing only a pick 1 bucket and 1 log that is recoverable at a later date. Hostile biome safe. Note screen caps are not from a barren biome so ignore tree/shrub growths, Didn't use any for the breach.
The first thing you must do is yourself safely underground. Once you've accomplished that Dig an offshoot from your base to where you want the breach to be. The footprint up to the surface will be 9x9 with an underground footprint of 10x10 mostly to control flooding from the splashdown. Z lvl 0 for this example is the layer directly above the aquifer, z-1 is first aquifer Z-2 second aquifer Z+1 first soil layer and Z+2 is the surface.
Designate a 9x9 of upstairs on Z-0 Centerd in that designation an 8x8 of normal dig, in the very center an up/down stair. On Z+1 designate up/down stairs over all of the stairs from the level below. On Z+1 also designate a path so you can access this area later, it will be where you trigger the cavein from. Note I had 2 additional channels on Z+1 in the screenshots that proved redundant.
Channel out some of the walls surrounding the stairs on Z-0. Leave an access path so you can still get in here. These channels catch water during the cavein to reduce how far the flood enters your base.
Now for the critical part. Your going to have to do a chickenrun to reach the second layer of the aquifer. In the center of of the area under the up/down stair designate an updown on Z-1. you will want to use the one step as your miner is diging. As soon as the tile clears you need to designate a second up/down on Z-2. If you dont 1 step this the chamber will flood before your miner can dig into the second layer of the aquifer and you'll have to start over in a new spot. Your miner will also need to be skilled up. I did it with my dwarf that had the best str/agility stats at miner level 12. At lvl 10 he only had a 50 50 chance of getting it done. Make sure your miner is always digging to skill up and do a test run of the chickenrun somewhere else to make sure he can pull it off.
first designation
Chickenrun maneuver successful.
Thats the hard part. If you've gotten this far your mostly home free as long as undead flyers dont get you later when you expose to the surface. On Z-1 order the 8 squares adjacent to your up/down stair drain channeled out. This will result in both layers of the aquifer having empty squares here. Careful not to channel out the stairs at the same time or you'll drown your miner and lose your pick.
now for the risky part. From here on out your workers will be exposed to flyers although land based monsters should never have access to your dwarves. On the surface (Z+2) Designate channels over all the upstairs. Your miner can access them from below thanks to the upstairs on Z+1 but there will never be a walkable path into your base even as your channeling.
Before
After
Next Channel out all the stairs on Z+1 except for the one next to your access path on that level. This stair is your trigger for the cavein. Don't forget the stair in the center.
Remove all the upstairs on Z-0
Channel out the splashdown area. Despite what the image shows I suggest you do this one row at a time to avoid miner accidents. Technically you could do this step before opening your work area to the surface.
Were ready to pull the trigger.
Channel out the remaining upstair on Z+1. On my map I tried channeling out the tile before(between the 2 open spaces) for miner safety. turns out the stair was attached to the surface ground. I had to build a temporary floor to get at it. I would recommend you give the pick to a different dwarf. There is a small chance he could get blasted into the wall by the cave in and die.
Splash
If you haven't made your bucket by this point do so now. Designate a water zone next to the 3x3 full of water, Dispose of it however you see fit. I dug an up stair to Z+1 and dumped the water from there back into the aquifer.
Once the water is down to 3 deep you can channel out the ring around the 3x3 and the rest of that layer should evaporate on its own. This also gives you a convenient down-ramp to the next level.
Sadly you can not designate a water source next to the up/down stairs on this level so channel out the stair.
get your bucket master back to hauling the last 6 buckets worth out of the center tile.
Use one of your remaining logs to rebuild the downstairs so you can access the next level down. You can recover this log later once you have stone.
Congratulations. Now that the stair is once again connected your miner can dig strait down under the aquifer. And you only lost a single log permanently. With proper juggling of resources you can setup a butchery Butcher your draft animals and even make a barrel to store some of the food in while your finishing your aquifer pierce. You will need to recover the log from your downstairs before you can make your axe but that shouldn't be too hard.