As you can see in the parts page link below....lots of bits to this thing.
It's been awhile too since I rebuilt one of these so memory fades a bit. But I remember that repairing them isn't as daunting as the picture indicates.
https://www.boats.net/catalog/honda...p/bf20dk3-srta-2007-and-later/power-trim-tilt
To pinpoint the leak you may need to separate the trim from the outboard. This requires splitting the stern bracket and removing one side. I believe it's the stbd side but...it's been awhile.
Before doing that though, check the manual tilt valve and drain plug orings (23 and 24 in the parts list)
Don't try doing this over the water! Those are common leak points and could indicate a rebuild is needed as well but you might just get away with an EZ fix here. Much care must be taken not to lose parts or get things out of order...of course!
The other place is, of course, the cylinder piston seal.
While most Dexxron fluid is "backwards compatible" I would stay clear of the V (5) and Vl (6) renditions for servicing this trim. In my experience with hydraulic systems, I have encountered some some warnings about using those sophisticated transmission fluids in straight up pumping systems. Dexxron lll (3) is still readily available at most auto parts retailers and is a commonly used hydraulic pump fluid going back many years. The old "F type" fluid will work too...if you can find it. Also, "power steering fluid" would probably do in a pinch with no harm. Just use a "major brand"...like Lucas... if you do.
If you do end up disassembling this, you should also install new brushes in the motor and seal the point of entry for the power wires with Permatex "Right Stuff" sealer/gasket maker.
CAUTION: DO NOT USE SILICONE SEALER CONTAINING ACETIC ACID (smells like vinegar) FOR SEALING ELECTRICAL COMPONENTS OR WHERE THE ACID CURE CAN "POISON" SENSITIVE DEVICES LIKE OXYGEN (O2) AND AIR/FUEL RATIO (AFR) SENSORS!
I'll leave you with this: Once these units get air in them, they can be very difficult to get get properly bled. It takes a lot of patience and can be a bit worrisome as you're going through the process. But it's totally doable and will eventually work out if you just keep at it.
Good luck.