[sentence]。尽管如此,[subject] + 还是 / 仍然 / 依然 + [verb phrase]
[sentence]。即便如此,[subject] + 也 + [verb phrase]
尽管如此 starts a new sentence and turns against the one before it. 如此 means "so, like this" and points back at the fact just stated; the sentence after it says what happened anyway. It belongs to writing and formal speech.
The second sentence usually carries 还是, 仍然, 依然 or 却 before the verb, the same way a 尽管 clause is answered.
尽管 opens a clause inside one sentence and needs the fact after it. 尽管如此 already holds the fact in 如此, so it stands alone at the start of the next sentence with a comma after it.
即便如此 says the same thing with a hypothetical edge: "even if that's so". It takes 也 rather than 还是. 虽然如此 also exists but reads stiffer than either.
尽管如此 needs a fact that should have stopped what follows. When the second sentence is the natural result, the link is 因此 or 所以.