mine had a similar leak. I went and moved all fish/plants to a bucket. soil/gravel to another, wrapped filter pump with sponge and left it spraying on the bio filter in the fish bucket. (heater also in the fish one)
clean/dry working surface, also mark where filter divider (plastic) meets glass from outside with a permanent marker (rubbing alcohol removes it so no worries) this will come in handy later.
put one side standard blade (like the one you use for construction and such) through entire caulking then shaved off extra by finger nail.
glass surface: use the square corner against glass @ 60-70 degree angle and pull toward your body from one edge to another, this way the old caulk is removed as much.
remove as much as possible by using this blade, caulk on caulk does not provide good adhesion also when you smooth the surface it causes bubbling.
so I followed by cleaning with acetone (on glass) rubbing alcohol for plastic part.
(took about 30min from wiped dry empty tank to this point)
taped all edges with 6mm or so gap on the meeting surface on both side with masking tape (blue or whatever color it comes) |tape| |corner| |tape| <-- gap is about how much I left open.
dub some alcohol on a kitchen paper towel final wipe the grease from your finger (use a glove if you wish)
put the caulking without gap or bubble. I have cut the tip just about as wide as the previously shown distance (about 6mm/ 1/4 in opening), with a constant pressure to a gun or tube, start from one end then "push" the tip to the next. By pushing tip and moving excess amount onto the joint you can make sure the constant stream of caulk to be deposited onto the joint. (I think...)
Do this relatively quick if you are going to finish all at once. 5-10min include smoothing the surface.
To smooth the surface, run finger tip (thumb perpendicular to the corner) so the caulk will be y=1/x graph shape. (look up reciprocal curve, if not familiar)
Make sure there is no gap, no bubble etc when you do this.
before curing remove the tape carefully without touching any of the uncured caulk.
As for the filter section divider (which was pain in the A$$ imo)
As soon as you remove the tape which comes in contact lay caulking on constant line along with the previously marked line on the outside of the tank (the permanent marker line) about 6mm wide line as straight as possible, heavier on top of the tank.
once 4 meeting surface is caulked (2 sides, bottom and back) drop in the plastic part from top, caulking materials will be pushed down but do not worry at this point.
use metal chopstick (or similar with 6mm or so square stick would do) run the vertical sides from bottom up. also lightly push on the plastic as you do this so the parts wont wiggle.
remove excess as you do one line before another one.
do all meeting surface like this.
If you haven't done the front (across from the filter end) do that and caulking is done.
leave the tank in well vented location (near window with a fan on it) for 2 full days.
put the tank on a flat surface filled up water and leak test over night (since animal/plants in a bucket still)
All worked and zero loss on critters. tank is up and running.
** used half of the bucket water in the newly sealed tank, filled other with pretreated water. start with decoration and transfer heater in the main viewing section (to heat up water quick enough.)
once all good to go all the other goes in like you just bought a new fish/shrimp etc...
Bump: Sorry it was long and hard to read...