So I’ve restored and strengthened (I can stand on top of it and weigh 95kg) this tall boy ready for my tank
Unsure how big the aquarium is but just remember it's not just the weight of the water but also the weight of the glass aquarium itself, also remember over time weighty objects have an effect on things, especially if the weight is more direct like with the legs.
What I would be most concerned about is the leg circled in red; from what I can see in the photo there seems to be a joists running roughly where the red lines are (I'm sure there will also be one near the wall assuming it's an original stone one) this leg is also near to the edge of the board. If you have a cellar or access underneath you can inspect the board to make sure it is square easily enough and you could also add some noggins to reinforce things; some old floor boards are not square at the edges so have maybe half the thickness. Unsure about the other legs and this is only assuming my red lines are showing joists - looked like nails!
The planer will be coming out this week!
Unsure of your DIY skill set but planing the end grain of the wood is always a risky business; especially if it as an electric one!
Regardless of how you go about things it's always worth heavily scoring the wood with a sharp stanley blade to try and prevent splintering before planing.
The only way is to pack under the legs to get it the best you can. To get it perfect You can use wedges. Two wedges over lap and as you tap the ends it will lift the unit up.
Good method using folding wedges
Do you have any of those felt pads for going under furniture legs... that might help smooth out small inaccuracies...
Just be careful with these; if using a few stacked up they can compress over time, especially stacked up one on top of the other.
The way I would do things:
I would think about getting the cabinet in exactly the position you intend, maybe even mark this position with masking tape under the legs as move it an inch or two could completely change things.
When it's in it's final position put the aquarium on the top and fill it with a couple of inches of water then you can use this to help you get the cabinet level - water is the oldest and still best levelling method,
with some small packing pieces of anything solid pack the cabinet so the measurement from the top of the tank to the waterline is the same all of the way around then you know it's level.
measure the largest gap you have between the floor and the bottom of a leg and then find something you can use to then mark this measurement on all of the legs. an offcut of thin wood maybe.
If you can use this measuring gauge to go around each leg and mark each leg; on all 4 sides if possible as floorboards rarely sit flat and it is doubtful these measurements are square either.
Whichever way you choose to trim the ends I would recommend using a sharp stanley blade.
if they are only small amounts I would consider seeing if you have access to a belt sander, for larger amounts trim them with a saw first then sand like above.
Give the edges a quick sand off.
I'd consider putting some felt wedges under like
@Matt @ ScapeEasy suggests but only after you have trimmed the legs and look for ones that are almost as big as the legs else you are further narrowing the force
Put the aquarium back in exactly the same place as where you marked it.